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Stein-fillable open books of genus one that do not admit positive factorisations 不允许正因式的一属斯坦因可填充开卷
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a4
Vitalijs Brejevs, Andy Wand
{"title":"Stein-fillable open books of genus one that do not admit positive factorisations","authors":"Vitalijs Brejevs, Andy Wand","doi":"10.4310/mrl.2023.v30.n3.a4","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a4","url":null,"abstract":"We construct an infinite family of genus one open book decompositions supporting Stein-fillable contact structures and show that their monodromies do not admit positive factorisations. This extends a line of counterexamples in higher genera and establishes that a correspondence between Stein fillings and positive factorisations only exists for planar open book decompositions.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"4 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138682067","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}
引用次数: 0
Zero–one laws for eventually always hitting points in rapidly mixing systems 快速混合系统中最终总是命中点的零一定律
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a7
Dmitry Kleinbock, Ioannis Konstantoulas, Florian K. Richter
{"title":"Zero–one laws for eventually always hitting points in rapidly mixing systems","authors":"Dmitry Kleinbock, Ioannis Konstantoulas, Florian K. Richter","doi":"10.4310/mrl.2023.v30.n3.a7","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a7","url":null,"abstract":"In this work we study the set of eventually always hitting points in shrinking target systems. These are points whose long orbit segments eventually hit the corresponding shrinking targets for all future times. We focus our attention on systems where translates of targets exhibit near perfect mutual independence, such as Bernoulli schemes and the Gauß map. For such systems, we present tight conditions on the shrinking rate of the targets so that the set of eventually always hitting points is a null set (or co‑null set respectively).","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"19 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681922","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}
引用次数: 0
A theorem on Hermitian rank and mapping problems 关于赫米秩和映射问题的定理
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a12
Ming Xiao
{"title":"A theorem on Hermitian rank and mapping problems","authors":"Ming Xiao","doi":"10.4310/mrl.2023.v30.n3.a12","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a12","url":null,"abstract":"In this paper, we first prove a Huang’s lemma type result. Then we discuss its applications in studying rigidity problems of mappings into indefinite hyperbolic spaces and bounded symmetric domains.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"19 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681986","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}
引用次数: 0
Annihilators of $D$-modules in mixed characteristic 混合特征中 $D$ 模块的湮没器
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a5
Rankeya Datta, Nicholas Switala, Wenliang Zhang
{"title":"Annihilators of $D$-modules in mixed characteristic","authors":"Rankeya Datta, Nicholas Switala, Wenliang Zhang","doi":"10.4310/mrl.2023.v30.n3.a5","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a5","url":null,"abstract":"Let $R$ be a polynomial or formal power series ring with coefficients in a DVR $V$ of mixed characteristic with a uniformizer $pi$. We prove that the $R$-module annihilator of any nonzero $mathcal{D}(R,V)$-module is either zero or is generated by a power of $pi$. In contrast to the equicharacteristic case, nonzero annihilators can occur; we give an example of a top local cohomology module of the ring $mathbb{Z}_2 [[x_0, dotsc, x_5]]$ that is annihilated by $2$, thereby answering a question of Hochster in the negative. The same example also provides a counterexample to a conjecture of Lyubeznik and Yildirim.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"172 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681996","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}
引用次数: 0
A Riemannian metric on hyperbolic components 双曲分量上的黎曼度量
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a6
Yan Mary He, Hongming Nie
{"title":"A Riemannian metric on hyperbolic components","authors":"Yan Mary He, Hongming Nie","doi":"10.4310/mrl.2023.v30.n3.a6","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a6","url":null,"abstract":"We introduce a Riemannian metric on certain hyperbolic components in the moduli space of degree at least $2$ rational maps in one complex variable. Our metric is constructed by considering the measure-theoretic entropy of a rational map with respect to some equilibrium state.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"33 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138682000","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}
引用次数: 0
Generalized Price’s law on fractional-order asymptotically flat stationary spacetimes 分数阶渐近平坦静止时空中的广义普赖斯定律
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-12-15 DOI: 10.4310/mrl.2023.v30.n3.a10
Katrina Morgan, Jared Wunsch
{"title":"Generalized Price’s law on fractional-order asymptotically flat stationary spacetimes","authors":"Katrina Morgan, Jared Wunsch","doi":"10.4310/mrl.2023.v30.n3.a10","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n3.a10","url":null,"abstract":"We obtain estimates on the rate of decay of a solution to the wave equation on a stationary spacetime that tends to Minkowski space at a rate $O ({lvert x rvert}^{-kappa}), kappa in (1,infty) backslash mathbb{N}$. Given suitably smooth and decaying initial data, we show a wave locally enjoys the decay rate $O(t^{-kappa-2+epsilon})$.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"92 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681991","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}
引用次数: 0
Counting quintic fields with genus number one 数属数为1的五次域
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-09-13 DOI: 10.4310/mrl.2023.v30.n2.a9
Kevin J. McGown, Frank Thorne, Amanda Tucker
{"title":"Counting quintic fields with genus number one","authors":"Kevin J. McGown, Frank Thorne, Amanda Tucker","doi":"10.4310/mrl.2023.v30.n2.a9","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n2.a9","url":null,"abstract":"We prove several results concerning genus numbers of quintic fields: we compute the proportion of quintic fields with genus number one; we prove that a positive proportion of quintic fields have arbitrarily large genus number; and we compute the average genus number of quintic fields. All of these results also hold when restricted to $S_5$-quintic fields only.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"14 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138509869","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}
引用次数: 2
On type II degenerations of hyperkähler manifolds hyperkähler流形的II型退化
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-06-21 DOI: 10.4310/mrl.2023.v30.n1.a6
D. Huybrechts, M. Mauri
{"title":"On type II degenerations of hyperkähler manifolds","authors":"D. Huybrechts, M. Mauri","doi":"10.4310/mrl.2023.v30.n1.a6","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n1.a6","url":null,"abstract":"We give a simple argument to prove Nagai’s conjecture for type II degenerations of compact hyperkähler manifolds and cohomology classes of middle degree. Under an additional assumption, the techniques yield the conjecture in arbitrary degree. This would complete the proof of Nagai’s conjecture in general, as it was proved already for type I degenerations by Kollár, Laza, Saccà, and Voisin [<b>10</b>] and independently by Soldatenkov [<b>18</b>], while it is immediate for type III degenerations. Our arguments are close in spirit to a recent paper by Harder [<b>8</b>] proving similar results for the restrictive class of good degenerations.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"13 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138509870","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}
引用次数: 0
On the distribution of multiplicatively dependent vectors 关于乘相关向量的分布
3区 数学
Mathematical Research Letters Pub Date : 2023-01-01 DOI: 10.4310/mrl.2023.v30.n2.a7
Sergei V. Konyagin, Min Sha, Igor E. Shparlinski, Cameron L. Stewart
{"title":"On the distribution of multiplicatively dependent vectors","authors":"Sergei V. Konyagin, Min Sha, Igor E. Shparlinski, Cameron L. Stewart","doi":"10.4310/mrl.2023.v30.n2.a7","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n2.a7","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135403482","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}
引用次数: 0
Rigidity of rationally connected smooth projective varieties from dynamical viewpoints 从动力学角度看合理连通光滑射影变的刚性
3区 数学
Mathematical Research Letters Pub Date : 2023-01-01 DOI: 10.4310/mrl.2023.v30.n2.a10
Sheng Meng, Guolei Zhong
{"title":"Rigidity of rationally connected smooth projective varieties from dynamical viewpoints","authors":"Sheng Meng, Guolei Zhong","doi":"10.4310/mrl.2023.v30.n2.a10","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n2.a10","url":null,"abstract":"Let $X$ be a rationally connected smooth projective variety of dimension $n$. We show that $X$ is a toric variety if and only if $X$ admits an int-amplified endomorphism with totally invariant ramification divisor. We also show that $Xcong (mathbb{P}^1)^{times n}$ if and only if $X$ admits a surjective endomorphism $f$ such that the eigenvalues of $f^*|_{text{N}^1(X)}$ (without counting multiplicities) are $n$ distinct real numbers greater than $1$.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"190 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136297298","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}
引用次数: 8
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