发布求助
文献互助 智能选刊 最新文献

Quarterly Journal of Mathematics最新文献

筛选
英文 中文
Induced almost para-Kähler Einstein metrics on cotangent bundles 共切束上的诱导几乎副卡勒爱因斯坦度量
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-09-14 DOI: 10.1093/qmath/haae047
Andreas Čap, Thomas Mettler
{"title":"Induced almost para-Kähler Einstein metrics on cotangent bundles","authors":"Andreas Čap, Thomas Mettler","doi":"10.1093/qmath/haae047","DOIUrl":"https://doi.org/10.1093/qmath/haae047","url":null,"abstract":"In earlier work, we have shown that for certain geometric structures on a smooth manifold M of dimension n, one obtains an almost para-Kähler–Einstein metric on a manifold A of dimension 2n associated to the structure on M. The geometry also associates a diffeomorphism between A and $T^*M$ to any torsion-free connection compatible with the geometric structure. Hence we can use this construction to associate to each compatible connection an almost para-Kähler–Einstein metric on $T^*M$. In this short article, we discuss the relation of these metrics to Patterson–Walker metrics and derive explicit formulae for them in the cases of projective, conformal and Grassmannian structures.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Sumsets in the set of squares 正方形集合中的和集
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-09-05 DOI: 10.1093/qmath/haae044
Christian Elsholtz, Lena Wurzinger
{"title":"Sumsets in the set of squares","authors":"Christian Elsholtz, Lena Wurzinger","doi":"10.1093/qmath/haae044","DOIUrl":"https://doi.org/10.1093/qmath/haae044","url":null,"abstract":"We study sumsets $mathcal{A}+mathcal{B}$ in the set of squares $mathcal{S}$ (and, more generally, in the set of kth powers $mathcal{S}_k$, where $kgeq 2$ is an integer). It is known by a result of Gyarmati that $mathcal{A}+mathcal{B}subset mathcal{S}_k cap [1,N]$ implies that $min(|mathcal{A}|,|mathcal{B}|)=O_k(log N)$. Here, we study how the upper bound on $|mathcal{B}|$ decreases, when the size of $|mathcal{A}|$ increases (or vice versa). In particular, if $|mathcal{A}|geq C k^{frac{1}{m}} m (log N)^{frac{1}{m}}$, then $|mathcal{B}|=O_k(m^2 log N)$, for sufficiently large N, a positive integer m and an explicit constant C > 0. For example, with $msim log log N$ this gives: If $|mathcal{A}|geq C_k log log N$, then $|mathcal{B}|=O_k(log N (log log N)^2)$.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Sinha’s spectral sequence for long knots in codimension one and non-formality of the little 2-disks operad 辛哈的一维长节谱序列和小二盘运算符的非形式性
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-08-13 DOI: 10.1093/qmath/haae043
Syunji Moriya
{"title":"Sinha’s spectral sequence for long knots in codimension one and non-formality of the little 2-disks operad","authors":"Syunji Moriya","doi":"10.1093/qmath/haae043","DOIUrl":"https://doi.org/10.1093/qmath/haae043","url":null,"abstract":"We compute some differentials of Sinha’s spectral sequence for cohomology of the space of long knots modulo immersions in codimension one, mainly over a field of characteristic 2 or 3. This spectral sequence is closely related to Vassiliev’s spectral sequence for the space of long knots in codimension $geq2$. We prove that the d2-differential of an element is non-zero in characteristic 2, which has already essentially been proved by Salvatore, and the d3-differential of another element is non-zero in characteristic 3. While the geometric meaning of the sequence is unclear in codimension one, these results have some applications to non-formality of operads. The result in characteristic 3 implies planar non-formality of the standard map $C_ast(E_1)to C_ast(E_2)$ in characteristic 3, where $C_ast(E_k)$ denotes the chain little k-disks operad. We also reprove the result of Salvatore which states that $C_ast(E_2)$ is not formal as a planar operad in characteristic 2 using the result in characteristic 2. For the computation, we transfer the structure on configuration spaces behind the spectral sequence onto Thom spaces over fat diagonals through a duality between configuration spaces and fat diagonals. This procedure enables us to describe the differentials by relatively simple maps to Thom spaces. We also show that the d2-differential of the generator of bidegree $(-4,2)$ is zero in characteristic $not=2$. This computation illustrates how one can manage the three-term relation using the description. Although the computations in this paper are concentrated to codimension one, our method also works for codimension $geq2$ and we prepare most of the basic notions and lemmas for general codimension.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 codegree isomorphism problem for finite simple groups 有限简单群的同度同构问题
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-07-11 DOI: 10.1093/qmath/haae039
Nguyen N Hung, Alexander Moretó
{"title":"The codegree isomorphism problem for finite simple groups","authors":"Nguyen N Hung, Alexander Moretó","doi":"10.1093/qmath/haae039","DOIUrl":"https://doi.org/10.1093/qmath/haae039","url":null,"abstract":"We study the codegree isomorphism problem for finite simple groups. In particular, we show that such a group is determined by the codegrees (counting multiplicity) of its irreducible characters. The proof is uniform for all simple groups and only depends on the classification by means of Artin–Tits’ simple order theorem.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141613702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Homotopy Theoretic Properties Of Open Books 开放书籍的同调理论特性
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-07-02 DOI: 10.1093/qmath/haae035
Ruizhi Huang, Stephen Theriault
{"title":"Homotopy Theoretic Properties Of Open Books","authors":"Ruizhi Huang, Stephen Theriault","doi":"10.1093/qmath/haae035","DOIUrl":"https://doi.org/10.1093/qmath/haae035","url":null,"abstract":"We study the homotopy groups of open books in terms of those of their pages and bindings. Under homotopy theoretic conditions on the monodromy we prove an integral decomposition result for the based loop space on an open book, and under more relaxed conditions we prove a rational loop space decomposition. The latter case allows for a rational dichotomy theorem for open books, as an extension of the classical dichotomy in rational homotopy theory. As a direct application, we show that for Milnor’s open book decomposition of an odd sphere with monodromy of finite order the induced action of the monodromy on the homology groups of its page cannot be nilpotent.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Non-commutative resolutions of linearly reductive quotient singularities 线性还原商奇点的非交换决议
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-06-21 DOI: 10.1093/qmath/haae033
Christian Liedtke, Takehiko Yasuda
{"title":"Non-commutative resolutions of linearly reductive quotient singularities","authors":"Christian Liedtke, Takehiko Yasuda","doi":"10.1093/qmath/haae033","DOIUrl":"https://doi.org/10.1093/qmath/haae033","url":null,"abstract":"We prove the existence of non-commutative crepant resolutions (in the sense of Van den Bergh) of quotient singularities by finite and linearly reductive group schemes in positive characteristic. In dimension 2, we relate these to resolutions of singularities provided by G-Hilbert schemes and F-blowups. As an application, we establish and recover results concerning resolutions for toric singularities, as well as canonical, log terminal and F-regular singularities in dimension 2.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Generic Diagonal Conic Bundles Revisited 通用对角线圆锥束再探讨
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-06-14 DOI: 10.1093/qmath/haae022
Alexei N Skorobogatov, Efthymios Sofos
{"title":"Generic Diagonal Conic Bundles Revisited","authors":"Alexei N Skorobogatov, Efthymios Sofos","doi":"10.1093/qmath/haae022","DOIUrl":"https://doi.org/10.1093/qmath/haae022","url":null,"abstract":"We prove a stronger form of our previous result that Schinzel’s Hypothesis holds for 100% of n-tuples of integer polynomials satisfying the usual necessary conditions, where the primes represented by the polynomials are subject to additional constraints in terms of Legendre symbols, as well as upper and lower bounds. We establish the triviality of the Brauer group of generic diagonal conic bundles over the projective line. Finally, we give an explicit lower bound for the probability that diagonal conic bundles in certain natural families have rational points.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Eventually fixed points of endomorphisms of virtually free groups 几乎自由群组内定点的最终定点
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-06-12 DOI: 10.1093/qmath/haae032
André Carvalho
{"title":"Eventually fixed points of endomorphisms of virtually free groups","authors":"André Carvalho","doi":"10.1093/qmath/haae032","DOIUrl":"https://doi.org/10.1093/qmath/haae032","url":null,"abstract":"We consider the subgroup of points of finite orbit through the action of an endomorphism of a finitely generated virtually free group, with particular emphasis on the subgroup of eventually fixed points, $text{EvFix}(varphi)$: points whose orbit contains a fixed point. We provide an algorithm to compute the subgroup of fixed points of an endomorphism of a finitely generated virtually free group and prove that finite orbits have cardinality bounded by a computable constant, which allows us to solve several algorithmic problems: deciding if φ is a finite order element of $text{End}(G)$, if φ is aperiodic, if $text{EvFix}(varphi)$ is finitely generated and if $text{EvFix}(varphi)$ is a normal subgroup. In the cases where $text{EvFix}(varphi)$ is finitely generated, we also present a bound for its rank and an algorithm to compute a generating set.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Motivic Geometry of two-Loop Feynman Integrals 双环费曼积分的动机几何学
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-06-10 DOI: 10.1093/qmath/haae015
Charles F Doran, Andrew Harder, Pierre Vanhove, Eric Pichon-Pharabod
{"title":"Motivic Geometry of two-Loop Feynman Integrals","authors":"Charles F Doran, Andrew Harder, Pierre Vanhove, Eric Pichon-Pharabod","doi":"10.1093/qmath/haae015","DOIUrl":"https://doi.org/10.1093/qmath/haae015","url":null,"abstract":"We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into mixed Tate pieces and the Hodge structures of families of hyperelliptic, elliptic or rational curves depending on the space-time dimension. For two-loop graphs with a small number of edges, we give more precise results. In particular, we recover a result of Bloch (Double box motive. SIGMA 2021;17,048) that in the well-known double-box example, there is an underlying family of elliptic curves, and we give a concrete description of these elliptic curves. We show that the motive for the non-planar two-loop tardigrade graph is that of a K3 surface. In an appendix by Eric Pichon-Pharabod, we argue via high-precision numerical computations that the Picard number of this K3 surface is generically 11 and we compute the expected lattice polarization. Lastly, we show that generic members of the ice cream cone family of graph hypersurfaces correspond to the pairs of sunset Calabi–Yau varieties.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On an ErdŐs–Kac-Type Conjecture of Elliott 论艾略特的一个埃尔德Ő斯-卡克型猜想
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2024-05-29 DOI: 10.1093/qmath/haae026
Ofir Gorodetsky, Lasse Grimmelt
{"title":"On an ErdŐs–Kac-Type Conjecture of Elliott","authors":"Ofir Gorodetsky, Lasse Grimmelt","doi":"10.1093/qmath/haae026","DOIUrl":"https://doi.org/10.1093/qmath/haae026","url":null,"abstract":"Elliott and Halberstam proved that $sum_{p lt n} 2^{omega(n-p)}$ is asymptotic to $phi(n)$. In analogy to the Erdős–Kac theorem, Elliott conjectured that if one restricts the summation to primes p such that $omega(n-p)le 2 log log n+lambda(2log log n)^{1/2}$ then the sum will be asymptotic to $phi(n)int_{-infty}^{lambda} mathrm{e}^{-t^2/2},mathrm{d}t/sqrt{2pi}$. We show that this conjecture follows from the Bombieri–Vinogradov theorem. We further prove a related result involving Poisson–Dirichlet distribution, employing deeper lying level of distribution results of the primes.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信