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Expositiones Mathematicae最新文献

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The Riemann–Roch theorem for the Adams operations Adams运算的Riemann-Roch定理
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-08-01 DOI: 10.1016/j.exmath.2023.07.002
A. Navarro , J. Navarro
{"title":"The Riemann–Roch theorem for the Adams operations","authors":"A. Navarro ,&nbsp;J. Navarro","doi":"10.1016/j.exmath.2023.07.002","DOIUrl":"10.1016/j.exmath.2023.07.002","url":null,"abstract":"<div><p>We prove the classical Riemann–Roch theorems for the Adams operations <span><math><mrow><mspace></mspace><msup><mrow><mi>ψ</mi></mrow><mrow><mi>j</mi></mrow></msup><mspace></mspace></mrow></math></span> on <span><math><mi>K</mi></math></span>-theory: a statement with coefficients on <span><math><mrow><mi>Z</mi><mrow><mo>[</mo><msup><mrow><mi>j</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>]</mo></mrow></mrow></math></span><span><span>, that holds for arbitrary projective morphisms, as well as another statement with </span>integral coefficients<span>, that is valid for closed immersions. In presence of rational coefficients, we also analyze the relation between the corresponding Riemann–Roch formula for one Adams operation and the analogous formula for the Chern character. To do so, we complete the elementary exposition of the work of Panin–Smirnov that was initiated by the first author in a previous paper. Their notion of oriented cohomology<span> theory on algebraic varieties allows to use classical arguments to prove general and neat statements, which imply all the aforementioned results as particular cases.</span></span></span></p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 4","pages":"Article 125513"},"PeriodicalIF":0.7,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44076407","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 Briançon–Skoda theorem for foliations 关于叶理的BriançOn–Skoda定理
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-07-20 DOI: 10.1016/j.exmath.2023.07.001
Arturo Fernández-Pérez , Evelia R. García Barroso , Nancy Saravia-Molina
{"title":"On Briançon–Skoda theorem for foliations","authors":"Arturo Fernández-Pérez ,&nbsp;Evelia R. García Barroso ,&nbsp;Nancy Saravia-Molina","doi":"10.1016/j.exmath.2023.07.001","DOIUrl":"10.1016/j.exmath.2023.07.001","url":null,"abstract":"<div><p>We generalize Mattei’s result relative to the Briançon–Skoda theorem for foliations to the family of foliations of the second type. We use this generalization to establish relationships between the Milnor and Tjurina numbers of foliations of second type, inspired by the results obtained by Liu for complex hypersurfaces and we determine a lower bound for the global Tjurina number of an algebraic curve.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 4","pages":"Article 125512"},"PeriodicalIF":0.7,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43076398","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 identity of Sylvester 以西尔维斯特的身份
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-06-25 DOI: 10.1016/j.exmath.2023.06.003
Bogdan Nica
{"title":"On an identity of Sylvester","authors":"Bogdan Nica","doi":"10.1016/j.exmath.2023.06.003","DOIUrl":"10.1016/j.exmath.2023.06.003","url":null,"abstract":"<div><p>We discuss an algebraic identity, due to Sylvester, as well as related algebraic identities and applications.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 4","pages":"Article 125511"},"PeriodicalIF":0.7,"publicationDate":"2023-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44956206","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
A matrix theory introduction to seaweed algebras and their index 海藻代数及其索引的矩阵论导论
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-06-19 DOI: 10.1016/j.exmath.2023.06.001
Alex Cameron , Vincent E. Coll Jr. , Nicholas Mayers , Nicholas Russoniello
{"title":"A matrix theory introduction to seaweed algebras and their index","authors":"Alex Cameron ,&nbsp;Vincent E. Coll Jr. ,&nbsp;Nicholas Mayers ,&nbsp;Nicholas Russoniello","doi":"10.1016/j.exmath.2023.06.001","DOIUrl":"10.1016/j.exmath.2023.06.001","url":null,"abstract":"<div><p><span>The index of a Lie algebra is an important algebraic invariant, but it is notoriously difficult to compute. However, for the suggestively-named seaweed algebras, the computation of the index can be reduced to a combinatorial formula based on the connected components of a “meander”: a </span>planar graph<span> associated with the algebra. Our index analysis on seaweed algebras requires only basic linear and abstract algebra. Indeed, the main goal of this article is to introduce a broader audience to seaweed algebras with minimal appeal to specialized language and notation from Lie theory. This said, we present several results that do not appear elsewhere and do appeal to more advanced language in the Introduction to provide added context.</span></p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 4","pages":"Article 125509"},"PeriodicalIF":0.7,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46797897","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 real-analytic Levi-flat hypersurfaces and holomorphic Webs 实解析Levi平超曲面与全纯Webs
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-06-13 DOI: 10.1016/j.exmath.2023.06.002
Ayane Adelina da Silva , Arturo Fernández-Pérez
{"title":"On real-analytic Levi-flat hypersurfaces and holomorphic Webs","authors":"Ayane Adelina da Silva ,&nbsp;Arturo Fernández-Pérez","doi":"10.1016/j.exmath.2023.06.002","DOIUrl":"10.1016/j.exmath.2023.06.002","url":null,"abstract":"<div><p><span>We investigate holomorphic webs tangent to real-analytic Levi-flat hypersurfaces on compact complex surfaces. Under certain conditions, we prove that a holomorphic web tangent to a real-analytic Levi-flat hypersurface admits a multiple-valued meromorphic first integral. We also prove that the Levi foliation of a Levi-flat hypersurface induced by an irreducible real-analytic curve in the Grassmannian </span><span><math><mrow><mi>G</mi><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span><span> extends to an algebraic web on the complex projective space.</span></p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 4","pages":"Article 125510"},"PeriodicalIF":0.7,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49053443","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 three general forms of multiple zeta(-star) values 关于多重zeta(-星)值的三种一般形式
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-06-01 DOI: 10.1016/j.exmath.2023.02.003
Kwang-Wu Chen , Minking Eie
{"title":"On three general forms of multiple zeta(-star) values","authors":"Kwang-Wu Chen ,&nbsp;Minking Eie","doi":"10.1016/j.exmath.2023.02.003","DOIUrl":"10.1016/j.exmath.2023.02.003","url":null,"abstract":"<div><p><span>In this paper, we investigate three general forms of multiple zeta(-star) values. We use these values to give three new sum formulas for multiple zeta(-star) values with height </span><span><math><mrow><mo>≤</mo><mn>2</mn></mrow></math></span> and the evaluation of <span><math><mrow><msup><mrow><mi>ζ</mi></mrow><mrow><mo>⋆</mo></mrow></msup><mrow><mo>(</mo><msup><mrow><mrow><mo>{</mo><mn>1</mn><mo>}</mo></mrow></mrow><mrow><mi>m</mi></mrow></msup><mo>,</mo><msup><mrow><mrow><mo>{</mo><mn>2</mn><mo>}</mo></mrow></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>. We also give a new proof of the sum formula of multiple zeta values.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 2","pages":"Pages 299-315"},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46179870","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
On Hasse’s inequality 关于Hasse不等式
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-06-01 DOI: 10.1016/j.exmath.2023.03.002
M. Ram Murty
{"title":"On Hasse’s inequality","authors":"M. Ram Murty","doi":"10.1016/j.exmath.2023.03.002","DOIUrl":"10.1016/j.exmath.2023.03.002","url":null,"abstract":"<div><p>We give an elementary exposition of the little known work of Harold Davenport related to Hasse’s inequality. We formulate a new conjecture suggested by this proof that has implications for the classical Riemann hypothesis.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 2","pages":"Pages 451-460"},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46346638","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
A simple algorithm for expanding a power series as a continued fraction 将幂级数展开为连分式的一个简单算法
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-06-01 DOI: 10.1016/j.exmath.2022.12.001
Alan D. Sokal
{"title":"A simple algorithm for expanding a power series as a continued fraction","authors":"Alan D. Sokal","doi":"10.1016/j.exmath.2022.12.001","DOIUrl":"10.1016/j.exmath.2022.12.001","url":null,"abstract":"<div><p>I present and discuss an extremely simple algorithm for expanding a formal power series as a continued fraction. This algorithm, which goes back to Euler (1746) and Viscovatov (1805), deserves to be better known. I also discuss the connection of this algorithm with the work of Gauss (1812), Stieltjes (1889), Rogers (1907) and Ramanujan, and a combinatorial interpretation based on the work of Flajolet (1980).</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 2","pages":"Pages 245-287"},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43473940","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: 6
Cartan’s method and its applications in sheaf cohomology Cartan方法及其在轴上同调中的应用
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-06-01 DOI: 10.1016/j.exmath.2023.02.001
Yuan Liu
{"title":"Cartan’s method and its applications in sheaf cohomology","authors":"Yuan Liu","doi":"10.1016/j.exmath.2023.02.001","DOIUrl":"10.1016/j.exmath.2023.02.001","url":null,"abstract":"<div><p><span>This paper aims to use Cartan’s original method in proving Theorems A and B on closed cubes to provide a different proof of the vanishing of sheaf cohomology over a closed cube if either (i) the degree exceeds its real dimension or (ii) the sheaf is (locally) constant and the degree is positive. In the first case, we can further use Godement’s argument to show the </span>topological dimension<span> of a paracompact topological manifold is less than or equal to its real dimension.</span></p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 2","pages":"Pages 288-298"},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41828343","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
Introducing memory to a family of multi-step multidimensional iterative methods with weight function 将记忆引入一类具有权函数的多步多维迭代方法
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2023-06-01 DOI: 10.1016/j.exmath.2023.04.004
Alicia Cordero , Eva G. Villalba , Juan R. Torregrosa , Paula Triguero-Navarro
{"title":"Introducing memory to a family of multi-step multidimensional iterative methods with weight function","authors":"Alicia Cordero ,&nbsp;Eva G. Villalba ,&nbsp;Juan R. Torregrosa ,&nbsp;Paula Triguero-Navarro","doi":"10.1016/j.exmath.2023.04.004","DOIUrl":"https://doi.org/10.1016/j.exmath.2023.04.004","url":null,"abstract":"<div><p>In this paper, we construct a derivative-free multi-step iterative scheme based on Steffensen’s method. To avoid excessively increasing the number of functional evaluations and, at the same time, to increase the order of convergence, we freeze the divided differences used from the second step and use a weight function on already evaluated operators. Therefore, we define a family of multi-step methods with convergence order <span><math><mrow><mn>2</mn><mi>m</mi></mrow></math></span>, where <span><math><mi>m</mi></math></span> is the number of steps, free of derivatives, with several parameters and with dynamic behaviour, in some cases, similar to Steffensen’s method. In addition, we study how to increase the convergence order of the defined family by introducing memory in two different ways: using the usual divided differences and the Kurchatov divided differences. We perform some numerical experiments to see the behaviour of the proposed family and suggest different weight functions to visualize with dynamical planes in some cases the dynamical behaviour.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"41 2","pages":"Pages 398-417"},"PeriodicalIF":0.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50204932","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
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