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Correction to the paper “The polynomial sieve and equal sums of like polynomials” (IMRN, Vol. 2015, No. 7, 1987–2019) 对论文 "多项式筛和同类多项式的等和 "的更正（《国际移动通信网络》，2015年第7期，1987-2019）
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-04-05 DOI: 10.1093/imrn/rnae066
Tim D Browning
{"title":"Correction to the paper “The polynomial sieve and equal sums of like polynomials” (IMRN, Vol. 2015, No. 7, 1987–2019)","authors":"Tim D Browning","doi":"10.1093/imrn/rnae066","DOIUrl":"https://doi.org/10.1093/imrn/rnae066","url":null,"abstract":"This paper corrects an error in an earlier work of the author.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575673","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}
引用次数: 0
The Moduli Space of Cyclic Covers in Positive Characteristic 正特征循环盖的模空间
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-04-05 DOI: 10.1093/imrn/rnae060
Huy Dang, Matthias Hippold
{"title":"The Moduli Space of Cyclic Covers in Positive Characteristic","authors":"Huy Dang, Matthias Hippold","doi":"10.1093/imrn/rnae060","DOIUrl":"https://doi.org/10.1093/imrn/rnae060","url":null,"abstract":"We study the $p$-rank stratification of the moduli space $operatorname{mathcal{A}mathcal{S}mathcal{W}}_{(d_{1},d_{2},ldots ,d_{n})}$, which represents $mathbb{Z}/p^{n}$-covers in characteristic $p>0$ whose $mathbb{Z}/p^{i}$-subcovers have conductor $d_{i}$. In particular, we identify the irreducible components of the moduli space and determine their dimensions. To achieve this, we analyze the ramification data of the represented curves and use it to classify all the irreducible components of the space. In addition, we provide a comprehensive list of pairs $(p,(d_{1},d_{2},ldots ,d_{n}))$ for which $operatorname{mathcal{A}mathcal{S}mathcal{W}}_{(d_{1},d_{2},ldots ,d_{n})}$ in characteristic $p$ is irreducible. Finally, we investigate the geometry of $operatorname{mathcal{A}mathcal{S}mathcal{W}}_{(d_{1},d_{2},ldots ,d_{n})}$ by studying the deformations of cyclic covers that vary the $p$-rank and the number of branch points.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575667","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}
引用次数: 0
Derived Equivalence for Elliptic K3 Surfaces and Jacobians 椭圆 K3 曲面的衍生等价性和雅各布数
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-04-04 DOI: 10.1093/imrn/rnae061
Reinder Meinsma, Evgeny Shinder
{"title":"Derived Equivalence for Elliptic K3 Surfaces and Jacobians","authors":"Reinder Meinsma, Evgeny Shinder","doi":"10.1093/imrn/rnae061","DOIUrl":"https://doi.org/10.1093/imrn/rnae061","url":null,"abstract":"We present a detailed study of elliptic fibrations on Fourier-Mukai partners of K3 surfaces, which we call derived elliptic structures. We fully classify derived elliptic structures in terms of Hodge-theoretic data, similar to the Derived Torelli Theorem that describes Fourier-Mukai partners. In Picard rank two, derived elliptic structures are fully determined by the Lagrangian subgroups of the discriminant group. As a consequence, we prove that for a large class of Picard rank 2 elliptic K3 surfaces all Fourier-Mukai partners are Jacobians, and we partially extend this result to non-closed fields. We also show that there exist elliptic K3 surfaces with Fourier-Mukai partners, which are not Jacobians of the original K3 surface. This gives a negative answer to a question raised by Hassett and Tschinkel.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575670","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}
引用次数: 0
Limiting Distribution of Dense Orbits in a Moduli Space of Rank m Discrete Subgroups in (m+1)-Space 级数为 m 的模数空间中密集轨道的极限分布 (m+1)- 空间中的离散子群
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-04-03 DOI: 10.1093/imrn/rnae046
Michael Bersudsky, Hao Xing
{"title":"Limiting Distribution of Dense Orbits in a Moduli Space of Rank m Discrete Subgroups in (m+1)-Space","authors":"Michael Bersudsky, Hao Xing","doi":"10.1093/imrn/rnae046","DOIUrl":"https://doi.org/10.1093/imrn/rnae046","url":null,"abstract":"We study the limiting distribution of dense orbits of a lattice subgroup $Gamma leq textrm{SL}(m+1,mathbb{R})$ acting on $Hbackslash textrm{SL}(m+1,mathbb{R})$, with respect to a filtration of growing norm balls. The novelty of our work is that the groups $H$ we consider have infinitely many non-trivial connected components. For a specific such $H$, the homogeneous space $Hbackslash G$ identifies with $X_{m,m+1}$, a moduli space of rank $m$-discrete subgroups in $mathbb{R}^{m+1}$. This study is motivated by the work of Shapira-Sargent who studied random walks on $X_{2,3}$.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575666","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}
引用次数: 0
Bounding Radon Numbers via Betti Numbers 通过贝蒂数限定拉顿数
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-04-03 DOI: 10.1093/imrn/rnae056
Zuzana Patáková
{"title":"Bounding Radon Numbers via Betti Numbers","authors":"Zuzana Patáková","doi":"10.1093/imrn/rnae056","DOIUrl":"https://doi.org/10.1093/imrn/rnae056","url":null,"abstract":"We prove general topological Radon-type theorems for sets in $mathbb R^{d}$ or on a surface. Combined with a recent result of Holmsen and Lee, we also obtain fractional Helly theorem, and consequently the existence of weak $varepsilon $-nets as well as a $(p,q)$-theorem for those sets. More precisely, given a family ${mathcal{F}}$ of subsets of ${mathbb{R}}^{d}$, we will measure the homological complexity of ${mathcal{F}}$ by the supremum of the first $lceil d/2rceil $ reduced Betti numbers of $bigcap{mathcal{G}}$ over all nonempty ${mathcal{G}} subseteq{mathcal{F}}$. We show that if ${mathcal{F}}$ has homological complexity at most $b$, the Radon number of ${mathcal{F}}$ is bounded in terms of $b$ and $d$. In case that ${mathcal{F}}$ lives on a surface and the number of connected components of $bigcap mathcal G$ is at most $b$ for any $mathcal Gsubseteq mathcal F$, then the Radon number of ${mathcal{F}}$ is bounded by a function depending only on $b$ and the surface itself. For surfaces, if we moreover assume the sets in ${mathcal{F}}$ are open, we show that the fractional Helly number of $mathcal F$ is linear in $b$. The improvement is based on a recent result of the author and Kalai. Specifically, for $b=1$ we get that the fractional Helly number is at most three, which is optimal. This case further leads to solving a conjecture of Holmsen, Kim, and Lee about an existence of a $(p,q)$-theorem for open subsets of a surface.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575507","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}
引用次数: 0
A Formalism of F-modules for Rings with Complete Local Finite F-Representation Type 具有完整局部有限 F 表示类型的环的 F 模块形式主义
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-04-02 DOI: 10.1093/imrn/rnae054
Eamon Quinlan-Gallego
{"title":"A Formalism of F-modules for Rings with Complete Local Finite F-Representation Type","authors":"Eamon Quinlan-Gallego","doi":"10.1093/imrn/rnae054","DOIUrl":"https://doi.org/10.1093/imrn/rnae054","url":null,"abstract":"We develop a formalism of unit $F$-modules in the style of Lyubeznik and Emerton-Kisin for rings that have finite $F$-representation type after localization and completion at every prime ideal. As applications, we show that if $R$ is such a ring then the iterated local cohomology modules $H^{n_{1}}_{I_{1}} circ cdots circ H^{n_{s}}_{I_{s}}(R)$ have finitely many associated primes, and that all local cohomology modules $H^{n}_{I}(R / gR)$ have closed support when $g$ is a nonzerodivisor on $R$.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575663","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}
引用次数: 0
Pentagram Rigidity for Centrally Symmetric Octagons 中心对称八角形的五角形刚性
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-04-02 DOI: 10.1093/imrn/rnae050
Richard Evan Schwartz
{"title":"Pentagram Rigidity for Centrally Symmetric Octagons","authors":"Richard Evan Schwartz","doi":"10.1093/imrn/rnae050","DOIUrl":"https://doi.org/10.1093/imrn/rnae050","url":null,"abstract":"In this paper I will establish a special case of a conjecture that intertwines the deep diagonal pentagram maps and Poncelet polygons. The special case is that of the $3$-diagonal map acting on affine equivalence classes of centrally symmetric octagons. The proof involves establishing that the map is Arnold-Liouville integrable in this case, and then exploring the Lagrangian surface foliation in detail.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602890","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}
引用次数: 0
Arithmetic Trialitarian Hyperbolic Lattices Are Not Locally Extended Residually Finite 算术试探性双曲晶格并非局部扩展残差有限
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-04-02 DOI: 10.1093/imrn/rnae053
Nikolay Bogachev, Leone Slavich, Hongbin Sun
{"title":"Arithmetic Trialitarian Hyperbolic Lattices Are Not Locally Extended Residually Finite","authors":"Nikolay Bogachev, Leone Slavich, Hongbin Sun","doi":"10.1093/imrn/rnae053","DOIUrl":"https://doi.org/10.1093/imrn/rnae053","url":null,"abstract":"A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $mathbf{PSO}_{7,1}(mathbb{R})$ are not LERF. This result, together with previous work by the third author, implies that no arithmetic lattice in $mathbf{PO}_{n,1}(mathbb{R})$, $n>3$, is LERF.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575669","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}
引用次数: 0
Decorated Discrete Conformal Maps and Convex Polyhedral Cusps 装饰离散共形映射和凸多面体顶点
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-04-02 DOI: 10.1093/imrn/rnae016
Alexander I Bobenko, Carl O R Lutz
{"title":"Decorated Discrete Conformal Maps and Convex Polyhedral Cusps","authors":"Alexander I Bobenko, Carl O R Lutz","doi":"10.1093/imrn/rnae016","DOIUrl":"https://doi.org/10.1093/imrn/rnae016","url":null,"abstract":"We discuss a notion of discrete conformal equivalence for decorated piecewise Euclidean surfaces (PE-surface), that is, PE-surfaces with a choice of circle about each vertex. It is closely related to inversive distance and hyperideal circle patterns. Under the assumption that the circles are non-intersecting, we prove the corresponding discrete uniformization theorem. The uniformization theorem for discrete conformal maps corresponds to the special case that all circles degenerate to points. Our proof relies on an intimate relationship between decorated PE-surfaces, canonical tessellations of hyperbolic surfaces and convex hyperbolic polyhedra. It is based on a concave variational principle, which also provides a method for the computation of decorated discrete conformal maps.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575676","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}
引用次数: 0
Minimal Diffeomorphisms with L1 Hopf Differentials 具有 L1 霍普夫微分的最小微分变形
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-04-02 DOI: 10.1093/imrn/rnae049
Nathaniel Sagman
{"title":"Minimal Diffeomorphisms with L1 Hopf Differentials","authors":"Nathaniel Sagman","doi":"10.1093/imrn/rnae049","DOIUrl":"https://doi.org/10.1093/imrn/rnae049","url":null,"abstract":"We prove that for any two Riemannian metrics $sigma _{1}, sigma _{2}$ on the unit disk, a homeomorphism $partial mathbb{D}to partial mathbb{D}$ extends to at most one quasiconformal minimal diffeomorphism $(mathbb{D},sigma _{1})to (mathbb{D},sigma _{2})$ with $L^{1}$ Hopf differential. For minimal Lagrangian diffeomorphisms between hyperbolic disks, the result is known, but this is the first proof that does not use anti-de Sitter geometry. We show that the result fails without the $L^{1}$ assumption in variable curvature. The key input for our proof is the uniqueness of solutions for a certain Plateau problem in a product of trees.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575505","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}
引用次数: 0
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