Mathematische Nachrichten最新文献

{"title":"Duality and the equations of Rees rings and tangent algebras","authors":"Matthew Weaver","doi":"10.1002/mana.70044","DOIUrl":"https://doi.org/10.1002/mana.70044","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math> be a module of projective dimension 1 over a Noetherian ring <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> and consider its Rees algebra <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {R}(E)$</annotation>\u0000 </semantics></math>. We study this ring as a quotient of the symmetric algebra <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {S}(E)$</annotation>\u0000 </semantics></math> and consider the ideal <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$mathcal {A}$</annotation>\u0000 </semantics></math> defining this quotient. In the case that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {S}(E)$</annotation>\u0000 </semantics></math> is a complete intersection ring, we employ a duality between <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$mathcal {A}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {S}(E)$</annotation>\u0000 </semantics></math> in order to study the Rees ring <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {R}(E)$</annotation>\u0000 </semantics></math> in multiple settings. In particular, when <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> is a complete intersection ring defined by quadrics, we consider its module of Kähler differentials <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Ω</mi>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>/</mo>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$Omega _{R/k}$</annotation>\u0000","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 10","pages":"3394-3416"},"PeriodicalIF":0.8,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145273078","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":"Spectral convergence of random regular graphs: Chebyshev polynomials, non-backtracking walks, and unitary-color extensions","authors":"Yulin Gong, Wenbo Li, Shiping Liu","doi":"10.1002/mana.70046","DOIUrl":"https://doi.org/10.1002/mana.70046","url":null,"abstract":"<p>In this paper, we extend a criterion of Sodin on the convergence of graph spectral measures to regular graphs of growing degree. As a result, we show that for a sequence of random <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>q</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(q_n+1)$</annotation>\u0000 </semantics></math>-regular graphs <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$G_n$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> vertices, if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>q</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mi>o</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$q_n = n^{o(1)}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>q</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$q_n$</annotation>\u0000 </semantics></math> tends to infinity, the normalized spectral measure converges almost surely in <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Wasserstein distance to the semicircle distribution for any <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>[</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$p in [1, infty)$</annotation>\u0000 </semantics></math>. This strengthens a result of Dumitriu and Pal. Many of the results are also extended to unitary-colored regular graphs. For example, we give a short proof of the weak convergence to the Kesten–McKay distribution for the normalized spectral measures of random <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math>-lifts. This result is derived by generalizing a formula of Friedman involving Chebyshev polynomials and non-","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 10","pages":"3417-3439"},"PeriodicalIF":0.8,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145273056","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":"General type results for moduli of deformation generalised Kummer varieties","authors":"Matthew Dawes","doi":"10.1002/mana.70043","DOIUrl":"https://doi.org/10.1002/mana.70043","url":null,"abstract":"<p>In Dawes [Algebr. Geom. 12(2025), no. 3, 601–660], families of orthogonal modular varieties <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mo>(</mo>\u0000 <mi>Γ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {F}(Gamma)$</annotation>\u0000 </semantics></math> associated with moduli spaces of compact hyperkähler manifolds of deformation generalized Kummer type (also known as <i>“deformation generalized Kummer varieties”</i>) were studied. The orthogonal modular varieties were defined for an even integer <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation>$2d$</annotation>\u0000 </semantics></math>, corresponding to the degree of polarization of the associated hyperkähler manifolds. It was shown in Dawes [Algebr. Geom. 12(2025), no. 3, 601–660] that the modular varieties are of general type when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation>$2d$</annotation>\u0000 </semantics></math> is square-free and sufficiently large. The purpose of this paper is to show that the square-free condition can be removed.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 10","pages":"3376-3393"},"PeriodicalIF":0.8,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145273076","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":"On discrete subgroups of the complex unit ball","authors":"Aeryeong Seo","doi":"10.1002/mana.70037","DOIUrl":"https://doi.org/10.1002/mana.70037","url":null,"abstract":"<p>In this paper, we study conditions for a discrete subgroup of the automorphism group of the <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-dimensional complex unit ball to be of convergence type or second kind, connecting these classifications to the existence of Green's functions and subharmonic or harmonic functions on its quotient space. Furthermore, we extend the definitions of convergence and divergence types to bounded symmetric domains, introducing a Poincaré series and providing a new criterion for discrete subgroups acting on these domains.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 10","pages":"3272-3286"},"PeriodicalIF":0.8,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272866","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":"The three-dimensional Seiberg–Witten equations for \u0000 \u0000 \u0000 3\u0000 /\u0000 2\u0000 \u0000 $3/2$\u0000 -spinors: A compactness theorem","authors":"Ahmad Reza Haj Saeedi Sadegh,&nbsp;Minh Lam Nguyen","doi":"10.1002/mana.70042","DOIUrl":"https://doi.org/10.1002/mana.70042","url":null,"abstract":"<p>The Rarita-Schwinger–Seiberg-Witten (RS–SW) equations are defined similarly to the classical Seiberg–Witten equations, where a geometric non–Dirac-type operator replaces the Dirac operator called the Rarita–Schwinger operator. In dimension 4, the RS–SW equation was first considered by the second author (Nguyen [J. Geom. Anal. 33(2023), no. 10, 336]). The variational approach will also give us a three-dimensional version of the equations. The RS–SW equations share some features with the multiple-spinor Seiberg–Witten equations, where the moduli space of solutions could be noncompact. In this paper, we prove a compactness theorem regarding the moduli space of solutions of the RS–SW equations defined on 3-manifolds.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 10","pages":"3331-3375"},"PeriodicalIF":0.8,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70042","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272771","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 large scaling property of level sets for degenerate \u0000 \u0000 p\u0000 $p$\u0000 -Laplacian equations with logarithmic BMO matrix weights","authors":"Thanh-Nhan Nguyen,&nbsp;Minh-Phuong Tran","doi":"10.1002/mana.70039","DOIUrl":"https://doi.org/10.1002/mana.70039","url":null,"abstract":"<p>In this study, we deal with generalized regularity properties for solutions to <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplace equations with degenerate matrix weights. It has been already observed in previous interesting works that gaining Calderón–Zygmund estimates for nonlinear equations with degenerate weights under the so-called <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>log</mi>\u0000 <mi>-</mi>\u0000 <mi>BMO</mi>\u0000 </mrow>\u0000 <annotation>$logtext{-}mathrm{BMO}$</annotation>\u0000 </semantics></math> condition and minimal regularity assumption on the boundary. In this paper, we also follow this direction and extend general gradient estimates for level sets of the gradient of solutions up to more subtle function spaces. In particular, we construct a covering of the super-level sets of the spatial gradient <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mo>∇</mo>\u0000 <mi>u</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <annotation>$|nabla u|$</annotation>\u0000 </semantics></math> with respect to a large scaling parameter via fractional maximal operators.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 10","pages":"3287-3306"},"PeriodicalIF":0.8,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272770","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":"Recurrence and transience for non-Archimedean and directed graphs","authors":"Matthias Keller,&nbsp;Anna Muranova","doi":"10.1002/mana.70040","DOIUrl":"https://doi.org/10.1002/mana.70040","url":null,"abstract":"<p>We introduce notions of recurrence and transience for graphs over a non-Archimedean ordered field. To achieve this, we establish a connection between these graphs and random walks on directed graphs over the reals. In particular, we give a characterization of the real directed graphs which can arise in such a way. As a main result, we give characterization for recurrence and transience in terms of a quantity related to the capacity.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 10","pages":"3307-3330"},"PeriodicalIF":0.8,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145273050","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":"On the optimization of the first weighted eigenvalue of the fractional Laplacian","authors":"Mrityunjoy Ghosh","doi":"10.1002/mana.70036","DOIUrl":"https://doi.org/10.1002/mana.70036","url":null,"abstract":"<p>In this paper, we consider the minimization problem for the first eigenvalue of the fractional Laplacian with respect to the weight functions lying in the rearrangement classes of fixed weight functions. We prove the existence of minimizing weights in the rearrangement classes of weight functions satisfying some assumptions. Also, we provide characterizations of these minimizing weights in terms of the eigenfunctions. Furthermore, we establish various qualitative properties, such as Steiner symmetry, radial symmetry, foliated Schwarz symmetry, etc., of the minimizing weights and corresponding eigenfunctions.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 10","pages":"3251-3271"},"PeriodicalIF":0.8,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272834","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":"Equidistribution of the eigenvalues of Hecke operators","authors":"Dohoon Choi,&nbsp;Min Lee,&nbsp;Youngmin Lee,&nbsp;Subong Lim","doi":"10.1002/mana.70033","DOIUrl":"https://doi.org/10.1002/mana.70033","url":null,"abstract":"<p>In this paper, we prove the equidistribution of the Hecke eigenvalues of Maass forms over an arbitrary number field at a fixed prime ideal, with respect to the Sato–Tate measure. As an application, we obtain that the proportion of Maass forms that do not satisfy the Ramanujan–Petersson conjecture at a fixed prime ideal is 0.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3210-3246"},"PeriodicalIF":0.8,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145038408","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":"Multiplicity and asymptotic behavior of normalized solutions for fourth-order equations of the Kirchhoff type","authors":"Tao Han,&nbsp;Hong-Rui Sun,&nbsp;Zhen-Feng Jin","doi":"10.1002/mana.70031","DOIUrl":"https://doi.org/10.1002/mana.70031","url":null,"abstract":"<p>In this paper, we study the following fourth-order equation of the Kirchhoff type\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 9","pages":"3172-3190"},"PeriodicalIF":0.8,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145038102","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}