Journal of the London Mathematical Society-Second Series最新文献

{"title":"Sidon sets from Erdős and Turán to yesterday","authors":"Imre Z. Ruzsa","doi":"10.1112/jlms.70702","DOIUrl":"https://doi.org/10.1112/jlms.70702","url":null,"abstract":"<p>Motivated by some problems in Fourier analysis, Sidon asked for the maximum number of integers in a block of given length with the property that their pairwise sums are all distinct. The first estimate is due to P. Erdős and P. Turán [J. Lond. Math. Soc. (1) <b>16</b> (1941), 212–215]. This started the theory of what came to be called “Sidon sets.” We present some classical gems and a couple of recent developments.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70702","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149048161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Metric spaces with small rough angles and the rectifiability of rough self-contracted curves","authors":"Estibalitz Durand Cartagena,&nbsp;Jeremy T. Tyson","doi":"10.1112/jlms.70691","DOIUrl":"https://doi.org/10.1112/jlms.70691","url":null,"abstract":"&lt;p&gt;The &lt;i&gt;small rough angle&lt;/i&gt; (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mo&gt;SRA&lt;/mo&gt;\u0000 &lt;annotation&gt;$operatorname{SRA}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) condition, introduced by Zolotov in &lt;span&gt;arXiv:1804.00234&lt;/span&gt;, captures the idea that all angles formed by triples of points in a metric space are small. In the first part of the paper, we develop the theory of metric spaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(X,d)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; satisfying the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;SRA&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{SRA}(alpha)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; condition for some &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$alpha &lt;1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Given a metric space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(X,d)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0&lt;alpha &lt;1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(X,d^alpha)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; satisfies the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;SRA&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70691","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148994006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The unipotent tropical fundamental group","authors":"Kyle Binder,&nbsp;Eric Katz","doi":"10.1112/jlms.70701","DOIUrl":"https://doi.org/10.1112/jlms.70701","url":null,"abstract":"<p>We prove that the unipotent completion of the fundamental group of the generic fiber of a tropically smooth family of algebraic varieties can be computed combinatorially: it is canonically isomorphic to the unipotent tropical fundamental group of its tropicalization, a concept that we introduce in this paper. We define the unipotent tropical fundamental group of a polyhedral complex in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math> as the Tannakian fundamental group of the category of unipotent tropical vector bundles with integrable connection. We show that it is computable in that it satisfies a Seifert–Van Kampen theorem and has a description for fans in terms of a bar complex. We then review an intermediate classical object, the unipotent log de Rham fundamental group. We prove our main result by establishing isomorphisms between the unipotent log de Rham fundamental group of the log closed fiber of the family and the unipotent topological and tropical fundamental groups by means of Kato–Nakayama spaces and a descent argument. Our arguments require a slight enlargement of the relevant categories, making use of enriched structures and partial compactifications.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148993996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tropical Donagi theorem","authors":"Felix Röhrle,&nbsp;Thomas Saillez","doi":"10.1112/jlms.70681","DOIUrl":"https://doi.org/10.1112/jlms.70681","url":null,"abstract":"<p>The tropical <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-gonal construction was introduced in recent work by the first author and D. Zakharov and structural results for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$n = 2,3$</annotation>\u0000 </semantics></math> were established. In this paper, we explore the construction for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$n = 4$</annotation>\u0000 </semantics></math> and prove a tropical analogue of Donagi's theorem which states that the tetragonal construction is a triality which preserves Prym varieties. This confirms the speculations in previous work and establishes new results on the non-injectivity of the tropical Prym–Torelli morphism. Finally, we demonstrate that the tropical <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-gonal construction is poorly behaved under edge contractions, thus preventing any immediate moduli-theoretic perspective.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70681","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148993997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some finiteness results on Oda's question for pairs of line bundles","authors":"He Xin","doi":"10.1112/jlms.70683","DOIUrl":"https://doi.org/10.1112/jlms.70683","url":null,"abstract":"&lt;p&gt;For a projective toric variety &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and nef line bundles &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$L_1, L_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on it, we prove some finiteness results related to Oda's question, which concerns the surjectivity of the multiplication map &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Φ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;⊗&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;⊗&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Phi _{L_1, L_2}: H^0(X, L_1)otimes H^0(X, L_2) rightarrow H^0(X, L_1otimes L_2)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. When &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Signature of the Milnor fiber of parametrized surfaces","authors":"R. Giménez Conejero,&nbsp;Gergő Pintér","doi":"10.1112/jlms.70699","DOIUrl":"https://doi.org/10.1112/jlms.70699","url":null,"abstract":"<p>We compute the signature of the Milnor fiber of certain type of nonisolated complex surface singularities, namely, images of finitely determined holomorphic germs. An explicit formula is given in algebraic terms. As a corollary we show that the signature of the Milnor fiber is a topological invariant for these singularities. The proof combines complex analytic and smooth topological techniques. The main tools are Thom–Mather theory of map germs and the Ekholm–Szűcs–Takase–Saeki formula for immersions. We give a table with many examples for which the signature is computed using our formula.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148943177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the integral simplicial volume of cyclic covers of mapping tori","authors":"Federica Bertolotti,&nbsp;Ervin Hadžiosmanović","doi":"10.1112/jlms.70697","DOIUrl":"https://doi.org/10.1112/jlms.70697","url":null,"abstract":"<p>In this paper, we investigate the asymptotic behavior of the integral simplicial volume of cyclic covers of manifolds that fiber over the circle with fiber given by an <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-dimensional torus. By studying the integral filling volume—an invariant introduced by Frigerio and the first author—for the monodromy, we establish both lower and upper bounds for the limit of the integral simplicial volume of these covers, normalized by the degree of the covering. These bounds are expressed in terms of the action of the monodromy on the real homology of the fiber. As applications, we establish a close connection between the topological entropy and the integral filling volume of self-homeomorphisms of <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$ n$</annotation>\u0000 </semantics></math>-dimensional tori, we find new examples for which the <span></span><math>\u0000 <semantics>\u0000 <mi>Δ</mi>\u0000 <annotation>$Delta$</annotation>\u0000 </semantics></math>-complexity and the integral simplicial volume are not equivalent, and we prove the nonvanishing of the filling volume for Anosov self-diffeomorphisms of infranilmanifolds.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70697","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148943176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new approach for the analysis of evolution partial differential equations on a finite interval","authors":"Türker Özsarı,&nbsp;Dionyssios Mantzavinos,&nbsp;Konstantinos Kalimeris","doi":"10.1112/jlms.70694","DOIUrl":"https://doi.org/10.1112/jlms.70694","url":null,"abstract":"<p>We show that, for certain evolution partial differential equations, the solution on a finite interval <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>ℓ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(0,ell)$</annotation>\u0000 </semantics></math> can be reconstructed as a superposition of restrictions to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>ℓ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(0,ell)$</annotation>\u0000 </semantics></math> of solutions to two associated partial differential equations posed on the half-lines <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(0,infty)$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mi>∞</mi>\u0000 <mo>,</mo>\u0000 <mi>ℓ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(-infty,ell)$</annotation>\u0000 </semantics></math>. Determining the appropriate data for these half-line problems amounts to solving an inverse problem, which we formulate via the unified transform of Fokas (also known as the Fokas method) and address via a fixed-point argument in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-based Sobolev spaces, including fractional ones through interpolation techniques. We illustrate our approach through two canonical examples, the heat equation and the Korteweg-de Vries (KdV) equation, and provide numerical simulations for the former example. We further demonstrate that the new approach extends to more general evolution partial differential equations, including those with time-dependent coefficients. A key outcome of this work is that spatial and temporal regularity estimates for problems on a finite interval can be directly derived from the corresponding estimates on the half-line. These results can, in turn, be used to establish local well-posedness for related nonlinear problems, as the essential ingredients are the linear estimates within nonlinear frameworks.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70694","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cartwright–Sturmfels Hilbert schemes","authors":"Ritvik Ramkumar,&nbsp;Alessio Sammartano","doi":"10.1112/jlms.70684","DOIUrl":"https://doi.org/10.1112/jlms.70684","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math> be the Cox ring of a product of <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math> projective spaces. In this paper, we study the Cartwright–Sturmfels Hilbert schemes of <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math>, which are multigraded Hilbert schemes that parameterize only radical ideals. Our main result shows that these Hilbert schemes are always smooth and irreducible if the Picard rank <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math> is at most 2. This result can be seen as a multigraded analogue of the famous theorems of Fogarty and Maclagan–Smith, where the Picard rank replaces the dimension of the ambient space.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70684","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"K-stability of del Pezzo surfaces with a single quotient singularity","authors":"In-Kyun Kim,&nbsp;Dae-Won Lee","doi":"10.1112/jlms.70687","DOIUrl":"https://doi.org/10.1112/jlms.70687","url":null,"abstract":"<p>In this paper, we study the K-stability of del Pezzo surfaces with a unique quotient singularity whose minimal resolution has exceptional locus <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$E_1+E_2$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>E</mi>\u0000 <mn>1</mn>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <mo>=</mo>\u0000 <mo>−</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$E_1^2=-n$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>E</mi>\u0000 <mn>2</mn>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <mo>=</mo>\u0000 <mo>−</mo>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$E_2^2=-m$</annotation>\u0000 </semantics></math>, and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>·</mo>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$E_1cdot E_2=1$</annotation>\u0000 </semantics></math> for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$n,mgeqslant 2$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}