Bulletin of the London Mathematical Society最新文献

{"title":"Cross-ratio degrees and triangulations","authors":"Rob Silversmith","doi":"10.1112/blms.13148","DOIUrl":"https://doi.org/10.1112/blms.13148","url":null,"abstract":"<p>The cross-ratio degree problem counts configurations of <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> points on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^1$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$n-3$</annotation>\u0000 </semantics></math> prescribed cross-ratios. Cross-ratio degrees arise in many corners of combinatorics and geometry, but their structure is not well-understood in general. Interestingly, examining various special cases of the problem can yield combinatorial structures that are both diverse and rich. In this paper, we prove a simple closed formula for a class of cross-ratio degrees indexed by triangulations of an <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-gon; these degrees are connected to the geometry of the real locus of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$M_{0,n}$</annotation>\u0000 </semantics></math>, and to positive geometry.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3518-3529"},"PeriodicalIF":0.8,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13148","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142574208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on limiting Calderon–Zygmund theory for transformed \u0000 \u0000 n\u0000 $n$\u0000 -Laplace systems in divergence form","authors":"Dorian Martino,&nbsp;Armin Schikorra","doi":"10.1112/blms.13147","DOIUrl":"https://doi.org/10.1112/blms.13147","url":null,"abstract":"<p>We consider rotated <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-Laplace systems on the unit ball <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$B_1 subset mathbb {R}^n$</annotation>\u0000 </semantics></math> of the form\u0000\u0000 </p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3502-3517"},"PeriodicalIF":0.8,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13147","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on the PDE approach to the \u0000 \u0000 \u0000 L\u0000 ∞\u0000 \u0000 $L^infty$\u0000 estimates for complex Hessian equations on transverse Kähler manifolds","authors":"P. Sivaram","doi":"10.1112/blms.13150","DOIUrl":"https://doi.org/10.1112/blms.13150","url":null,"abstract":"<p>In this note, the partial differential equation (PDE) approach of Guo–Phong–Tong and Guo–Phong–Tong–Wang adapted to prove an <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^infty$</annotation>\u0000 </semantics></math> estimate for transverse complex Monge–Ampère equations on homologically orientable transverse Kähler manifolds. As an application, a purely PDE-based proof of the regularity of Calabi–Yau cone metrics on <span></span><math>\u0000 <semantics>\u0000 <mi>Q</mi>\u0000 <annotation>$mathbb {Q}$</annotation>\u0000 </semantics></math>-Gorenstein <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$mathbb {T}$</annotation>\u0000 </semantics></math>-varieties is obtained.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3542-3564"},"PeriodicalIF":0.8,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Selberg identity for the Shimura lift","authors":"Hui Xue","doi":"10.1112/blms.13151","DOIUrl":"https://doi.org/10.1112/blms.13151","url":null,"abstract":"<p>We first prove a Selberg-type identity for the Shimura lift of the Rankin–Cohen bracket of a normalized Hecke eigenform and the theta function. We then discuss its relationship with the nonvanishing of central values of <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-functions associated to Hecke eigenforms.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3565-3579"},"PeriodicalIF":0.8,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13151","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142574038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Steenbrink-type vanishing for surfaces in positive characteristic","authors":"Tatsuro Kawakami","doi":"10.1112/blms.13146","DOIUrl":"https://doi.org/10.1112/blms.13146","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>B</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(X,B)$</annotation>\u0000 </semantics></math> be a pair of a normal surface over a perfect field of characteristic <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$p&amp;gt;0$</annotation>\u0000 </semantics></math> and an effective <span></span><math>\u0000 <semantics>\u0000 <mi>Q</mi>\u0000 <annotation>$mathbb {Q}$</annotation>\u0000 </semantics></math>-divisor <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math> on <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math>. We prove that Steenbrink-type vanishing holds for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>,</mo>\u0000 <mi>B</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(X,B)$</annotation>\u0000 </semantics></math> if it is log canonical and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 <annotation>$p&amp;gt;5$</annotation>\u0000 </semantics></math>, or it is <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-pure. We also show that rational surface singularities satisfying the vanishing are <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-injective.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3484-3501"},"PeriodicalIF":0.8,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chromatic symmetric functions and polynomial invariants of trees","authors":"José Aliste-Prieto,&nbsp;Jeremy L. Martin,&nbsp;Jennifer D. Wagner,&nbsp;José Zamora","doi":"10.1112/blms.13144","DOIUrl":"https://doi.org/10.1112/blms.13144","url":null,"abstract":"<p>Stanley asked whether a tree is determined up to isomorphism by its chromatic symmetric function. We approach Stanley's problem by studying the relationship between the chromatic symmetric function and other invariants. First, we prove Crew's conjecture that the chromatic symmetric function of a tree determines its generalized degree sequence, which enumerates vertex subsets by cardinality and the numbers of internal and external edges. Second, we prove that the restriction of the generalized degree sequence to subtrees contains exactly the same information as the subtree polynomial, which enumerates subtrees by cardinality and number of leaves. Third, we construct arbitrarily large families of trees sharing the same subtree polynomial, proving and generalizing a conjecture of Eisenstat and Gordon.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3452-3476"},"PeriodicalIF":0.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cyclic-Schottky strata of Schottky space","authors":"Rubén A. Hidalgo,&nbsp;Milagros Izquierdo","doi":"10.1112/blms.13141","DOIUrl":"https://doi.org/10.1112/blms.13141","url":null,"abstract":"&lt;p&gt;Schottky space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;${mathcal {S}}_{g}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$g geqslant 2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is an integer, is a connected complex orbifold of dimension &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$3(g-1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;; it provides a parametrization of the &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;PSL&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm PSL}_{2}({mathbb {C}})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-conjugacy classes of Schottky groups &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Γ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Gamma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of rank &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;annotation&gt;$g$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The branch locus &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;B&lt;/mi&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathcal {B}}_{g} subset {mathcal {S}}_{g}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, consisting of those conjugacy classes of Schottky groups being a finite index proper normal subgroup of some Kleinian group, is known to be connected. If &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;Γ&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3412-3427"},"PeriodicalIF":0.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13141","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On finite generation in magnitude (co)homology and its torsion","authors":"Luigi Caputi,&nbsp;Carlo Collari","doi":"10.1112/blms.13143","DOIUrl":"https://doi.org/10.1112/blms.13143","url":null,"abstract":"<p>The aim of this paper is to apply the framework developed by Sam and Snowden to study structural properties of graph homologies, in the spirit of Ramos, Miyata and Proudfoot. Our main results concern the magnitude homology of graphs introduced by Hepworth and Willerton, and we prove that it is a finitely generated functor (on graphs of bounded genus). More precisely, for graphs of bounded genus, we prove that magnitude cohomology, in each homological degree, has rank which grows at most polynomially in the number of vertices, and that its torsion is bounded. As a consequence, we obtain analogous results for path homology of (undirected) graphs.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3434-3451"},"PeriodicalIF":0.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13143","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regular maps from the lamplighter to metabelian groups","authors":"Antoine Gournay,&nbsp;Corentin Le Coz","doi":"10.1112/blms.13142","DOIUrl":"https://doi.org/10.1112/blms.13142","url":null,"abstract":"<p>We prove that the lamplighter group admits an injective Lipschitz map to any finitely generated metabelian group that is not virtually nilpotent. This implies that finitely generated metabelian groups satisfy the “analytically thin/analytically thick” dichotomy recently introduced by Hume, Mackay, and Tessera.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3428-3433"},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Classification conjectures for Leavitt path algebras","authors":"Guillermo Cortiñas,&nbsp;Roozbeh Hazrat","doi":"10.1112/blms.13139","DOIUrl":"https://doi.org/10.1112/blms.13139","url":null,"abstract":"<p>The theory of Leavitt path algebras is intrinsically related, via graphs, to the theory of symbolic dynamics and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$C^*$</annotation>\u0000 </semantics></math>-algebras where the major classification programs have been a domain of intense research in the last 50 years. In this article, we gather together current lines of research in the classification of Leavitt path algebras, questions, conjectures, and some of the results about them that have been obtained so far.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 10","pages":"3011-3060"},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13139","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142435063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}