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Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

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Local positivity and effective Diophantine approximation 局部正性和有效丢番图近似
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-11-08 DOI: 10.1007/s12188-022-00260-8
Matthias Nickel
{"title":"Local positivity and effective Diophantine approximation","authors":"Matthias Nickel","doi":"10.1007/s12188-022-00260-8","DOIUrl":"10.1007/s12188-022-00260-8","url":null,"abstract":"<div><p>In this paper we present a new approach to prove effective results in Diophantine approximation. This approach involves measures of local positivity of divisors combined with Faltings’s version of Siegel’s lemma instead of a zero estimate such as Dyson’s lemma. We then use it to prove an effective theorem on the simultaneous approximation of two algebraic numbers satisfying an algebraic equation with complex coefficients.\u0000</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 2","pages":"125 - 138"},"PeriodicalIF":0.4,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-022-00260-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50015028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On linear stability and syzygy stability 关于线性稳定性和系统稳定性
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-05-30 DOI: 10.1007/s12188-022-00258-2
Abel Castorena, Ernesto C. Mistretta, Hugo Torres-López
{"title":"On linear stability and syzygy stability","authors":"Abel Castorena,&nbsp;Ernesto C. Mistretta,&nbsp;Hugo Torres-López","doi":"10.1007/s12188-022-00258-2","DOIUrl":"10.1007/s12188-022-00258-2","url":null,"abstract":"<div><p>In previous works, the authors investigated the relationships between linear stability of a generated linear series |<i>V</i>| on a curve <i>C</i>, and slope stability of the syzygy vector bundle <span>(M_{V,L} := ker (V otimes mathcal {O}_C rightarrow L))</span>. In particular, the second named author and L. Stoppino conjecture that, for a complete linear system |<i>L</i>|, linear (semi)stability is equivalent to slope (semi)stability of <span>(M_{L})</span>. The first and third named authors proved that this conjecture holds in the two opposite cases: hyperelliptic and generic curves. In this work we provide a counterexample to this conjecture on any smooth plane curve of degree 7.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"91 - 103"},"PeriodicalIF":0.4,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-022-00258-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50104289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Triangular lat-igusa-todorov algebras 三角lat-igusa-todorov代数
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-05-24 DOI: 10.1007/s12188-022-00257-3
José Armando Vivero
{"title":"Triangular lat-igusa-todorov algebras","authors":"José Armando Vivero","doi":"10.1007/s12188-022-00257-3","DOIUrl":"10.1007/s12188-022-00257-3","url":null,"abstract":"<div><p>In 2021 the authors D. Bravo, M. Lanzilotta, O. Mendoza and J. Vivero gave a generalization of the concept of Igusa-Todorov algebra and proved that those algebras, named Lat-Igusa-Todorov (LIT for short), satisfy the finitistic dimension conjecture. In this paper we explore the scope of that generalization and give conditions for a triangular matrix algebra to be LIT in terms of the algebras and the bimodule used in its definition. As an application we obtain that the tensor product of an LIT <span>(mathbb {K})</span>-algebra with a path algebra of a quiver whose underlying graph is a tree, is LIT.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"53 - 67"},"PeriodicalIF":0.4,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50102451","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: 1
Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences 权值2的爱森斯坦级数的导数和模对应的交点
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-04-27 DOI: 10.1007/s12188-022-00256-4
Sungmun Cho, Shunsuke Yamana, Takuya Yamauchi
{"title":"Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences","authors":"Sungmun Cho,&nbsp;Shunsuke Yamana,&nbsp;Takuya Yamauchi","doi":"10.1007/s12188-022-00256-4","DOIUrl":"10.1007/s12188-022-00256-4","url":null,"abstract":"<div><p>We give a formula for certain values and derivatives of Siegel series and use them to compute Fourier coefficients of derivatives of the Siegel Eisenstein series of weight <span>(frac{g}{2})</span> and genus <i>g</i>. When <span>(g=4)</span>, the Fourier coefficient is approximated by a certain Fourier coefficient of the central derivative of the Siegel Eisenstein series of weight 2 and genus 3, which is related to the intersection of 3 arithmetic modular correspondences. Applications include a relation between weighted averages of representation numbers of symmetric matrices.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"27 - 52"},"PeriodicalIF":0.4,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-022-00256-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50049460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Fourier coefficients of the Siegel Eisenstein series of degree 2 with odd prime level, corresponding to the middle cusp 具有奇数素数阶的2次西格尔-爱森斯坦级数的傅里叶系数，对应于中间尖
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-01-18 DOI: 10.1007/s12188-021-00255-x
Keiichi Gunji
{"title":"Fourier coefficients of the Siegel Eisenstein series of degree 2 with odd prime level, corresponding to the middle cusp","authors":"Keiichi Gunji","doi":"10.1007/s12188-021-00255-x","DOIUrl":"10.1007/s12188-021-00255-x","url":null,"abstract":"<div><p>Let <i>p</i> be an odd prime. In this paper we compute the Fourier coefficients of the Siegel Eisenstein series of degree 2, level <i>p</i> with the trivial or the quadratic character, associated to a certain cusp. For that we need to define the <i>p</i>-factor of the special type of Siegel series with character.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"69 - 83"},"PeriodicalIF":0.4,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50036105","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: 2
Isotropicity of surfaces in Lorentzian 4-manifolds with zero mean curvature vector 平均曲率矢量为零的洛伦兹4流形中曲面的各向同性
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-01-03 DOI: 10.1007/s12188-021-00254-y
Naoya Ando
{"title":"Isotropicity of surfaces in Lorentzian 4-manifolds with zero mean curvature vector","authors":"Naoya Ando","doi":"10.1007/s12188-021-00254-y","DOIUrl":"10.1007/s12188-021-00254-y","url":null,"abstract":"<div><p>We already have the concept of isotropicity of a minimal surface in a Riemannian 4-manifold and a space-like or time-like surface in a neutral 4-manifold with zero mean curvature vector. In this paper, based on the understanding of it, we define and study isotropicity of a space-like or time-like surface in a Lorentzian 4-manifold <i>N</i> with zero mean curvature vector. If the surface is space-like, then the isotropicity means either the surface has light-like or zero second fundamental form or it is an analogue of complex curves in Kähler surfaces. In addition, if <i>N</i> is a space form, then the isotropicity means that the surface has both the properties. If the surface is time-like and if <i>N</i> is a space form, then the isotropicity means that the surface is totally geodesic.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"105 - 123"},"PeriodicalIF":0.4,"publicationDate":"2022-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-021-00254-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50010269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Set recognition of decomposable graphs and steps towards their reconstruction 设置可分解图的识别和重建步骤
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-01-03 DOI: 10.1007/s12188-021-00252-0
Bernd S. W. Schröder
{"title":"Set recognition of decomposable graphs and steps towards their reconstruction","authors":"Bernd S. W. Schröder","doi":"10.1007/s12188-021-00252-0","DOIUrl":"10.1007/s12188-021-00252-0","url":null,"abstract":"<div><p>It is proved that decomposable graphs are set recognizable and that the index graph of the canonical decomposition as well as the graphs induced on the maximal autonomous sets of vertices are set reconstructible. From these results, we obtain set reconstructibility for many decomposable graphs as well as a concise description of the decomposable graphs for which set reconstruction remains an open problem.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"1 - 25"},"PeriodicalIF":0.4,"publicationDate":"2022-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50006241","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: 2
A short note on sign changes and non-vanishing of Fourier coefficients of half-integral weight cusp forms 关于半积分权顶点形式的符号变化和傅里叶系数不消失的简短说明
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2021-12-14 DOI: 10.1007/s12188-021-00253-z
Winfried Kohnen
{"title":"A short note on sign changes and non-vanishing of Fourier coefficients of half-integral weight cusp forms","authors":"Winfried Kohnen","doi":"10.1007/s12188-021-00253-z","DOIUrl":"10.1007/s12188-021-00253-z","url":null,"abstract":"<div><p>We study sign changes and non-vanishing of a certain double sequence of Fourier coefficients of cusp forms of half-integral weight.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"92 1","pages":"85 - 90"},"PeriodicalIF":0.4,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-021-00253-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50025218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constant cycle and co-isotropic subvarieties in a Mukai system Mukai系统的常循环和共各向同性亚变体
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2021-11-10 DOI: 10.1007/s12188-021-00251-1
Isabell Hellmann
{"title":"Constant cycle and co-isotropic subvarieties in a Mukai system","authors":"Isabell Hellmann","doi":"10.1007/s12188-021-00251-1","DOIUrl":"10.1007/s12188-021-00251-1","url":null,"abstract":"<div><p>Combining theorems of Voisin and Marian, Shen, Yin and Zhao, we compute the dimensions of the orbits under rational equivalence in the Mukai system of rank two and genus two. We produce several examples of algebraically coisotropic and constant cycle subvarieties.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"91 2","pages":"199 - 224"},"PeriodicalIF":0.4,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-021-00251-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50018096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A model for random chain complexes 随机链配合物的一个模型
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2021-11-09 DOI: 10.1007/s12188-021-00248-w
Michael J. Catanzaro, Matthew J. Zabka
{"title":"A model for random chain complexes","authors":"Michael J. Catanzaro,&nbsp;Matthew J. Zabka","doi":"10.1007/s12188-021-00248-w","DOIUrl":"10.1007/s12188-021-00248-w","url":null,"abstract":"<div><p>We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over <span>(mathbb {F}_q)</span>, conditioned on ensuring that the composition of consecutive boundary maps is the zero map. We then investigate the combinatorial and homological properties of this random chain complex.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"91 2","pages":"335 - 344"},"PeriodicalIF":0.4,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-021-00248-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50016713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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