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A motivic study of generalized Burniat surfaces 广义燃烧曲面的动力学研究
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-11-01 DOI: 10.1007/s12188-018-0198-5
Chris Peters
{"title":"A motivic study of generalized Burniat surfaces","authors":"Chris Peters","doi":"10.1007/s12188-018-0198-5","DOIUrl":"10.1007/s12188-018-0198-5","url":null,"abstract":"<div><p>Generalized Burniat surfaces are surfaces of general type with <span>(p_g=q)</span> and Euler number <span>(e=6)</span> obtained by a variant of Inoue’s construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these surfaces. The method applies also to the so-called Sicilian surfaces introduced by Bauer et al. in (J Math Sci Univ Tokyo 22(2–15):55–111, 2015. arXiv:1409.1285v2). This implies that the Chow motives of all of these surfaces are finite-dimensional in the sense of Kimura.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"377 - 387"},"PeriodicalIF":0.4,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0198-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50000234","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
Modular forms for the (A_{1})-tower (A_{1}) -塔的模块化形式
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-10-10 DOI: 10.1007/s12188-018-0197-6
Martin Woitalla
{"title":"Modular forms for the (A_{1})-tower","authors":"Martin Woitalla","doi":"10.1007/s12188-018-0197-6","DOIUrl":"10.1007/s12188-018-0197-6","url":null,"abstract":"<div><p>In the 1960s Igusa determined the graded ring of Siegel modular forms of genus two. He used theta series to construct <span>(chi _{5})</span>, the cusp form of lowest weight for the group <span>({text {Sp}}(2,mathbb {Z}))</span>. In 2010 Gritsenko found three towers of orthogonal type modular forms which are connected with certain series of root lattices. In this setting Siegel modular forms can be identified with the orthogonal group of signature (2, 3) for the lattice <span>(A_{1})</span> and Igusa’s form <span>(chi _{5})</span> appears as the roof of this tower. We use this interpretation to construct a framework for this tower which uses three different types of constructions for modular forms. It turns out that our method produces simple coordinates.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"297 - 316"},"PeriodicalIF":0.4,"publicationDate":"2018-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0197-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50018310","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
A duality theorem for Tate–Shafarevich groups of curves over algebraically closed fields 代数闭域上曲线群的对偶定理
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-10-04 DOI: 10.1007/s12188-018-0196-7
Timo Keller
{"title":"A duality theorem for Tate–Shafarevich groups of curves over algebraically closed fields","authors":"Timo Keller","doi":"10.1007/s12188-018-0196-7","DOIUrl":"10.1007/s12188-018-0196-7","url":null,"abstract":"<div><p>In this note, we prove a duality theorem for the Tate–Shafarevich group of a finite discrete Galois module over the function field <i>K</i> of a curve over an algebraically closed field: there is a perfect duality of finite groups <img> for <i>F</i> a finite étale Galois module on <i>K</i> of order invertible in <i>K</i> and with <span>(F' = {{mathrm{Hom}}}(F,mathbf{Q}/mathbf {Z}(1)))</span>. Furthermore, we prove that <span>(mathrm {H}^1(K,G) = 0)</span> for <i>G</i> a simply connected, quasisplit semisimple group over <i>K</i> not of type <span>(E_8)</span>.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"289 - 295"},"PeriodicalIF":0.4,"publicationDate":"2018-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0196-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50015083","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
Semisimple weakly symmetric pseudo-Riemannian manifolds 半简单弱对称伪黎曼流形
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-08-29 DOI: 10.1007/s12188-018-0195-8
Zhiqi Chen, Joseph A. Wolf
{"title":"Semisimple weakly symmetric pseudo-Riemannian manifolds","authors":"Zhiqi Chen,&nbsp;Joseph A. Wolf","doi":"10.1007/s12188-018-0195-8","DOIUrl":"10.1007/s12188-018-0195-8","url":null,"abstract":"<div><p>We develop the classification of weakly symmetric pseudo-Riemannian manifolds <i>G</i> / <i>H</i> where <i>G</i> is a semisimple Lie group and <i>H</i> is a reductive subgroup. We derive the classification from the cases where <i>G</i> is compact, and then we discuss the (isotropy) representation of <i>H</i> on the tangent space of <i>G</i> / <i>H</i> and the signature of the invariant pseudo-Riemannian metric. As a consequence we obtain the classification of semisimple weakly symmetric manifolds of Lorentz signature <span>((n-1,1))</span> and trans-Lorentzian signature <span>((n-2,2))</span>.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"331 - 369"},"PeriodicalIF":0.4,"publicationDate":"2018-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0195-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50052486","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: 5
Non-vanishing of products of Fourier coefficients of modular forms of half-integral weight 半积分权值的模形式的傅里叶系数积的不消失
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-05-16 DOI: 10.1007/s12188-018-0194-9
Winfried Kohnen
{"title":"Non-vanishing of products of Fourier coefficients of modular forms of half-integral weight","authors":"Winfried Kohnen","doi":"10.1007/s12188-018-0194-9","DOIUrl":"10.1007/s12188-018-0194-9","url":null,"abstract":"<div><p>We prove a non-vanishing result in weight aspect for the product of two Fourier coefficients of a Hecke eigenform of half-integral weight.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 2","pages":"371 - 376"},"PeriodicalIF":0.4,"publicationDate":"2018-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0194-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50032824","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
Forms and currents defining generalized p-Kähler structures 定义广义p-Kähler结构的形式和电流
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-03-29 DOI: 10.1007/s12188-018-0193-x
Lucia Alessandrini
{"title":"Forms and currents defining generalized p-Kähler structures","authors":"Lucia Alessandrini","doi":"10.1007/s12188-018-0193-x","DOIUrl":"10.1007/s12188-018-0193-x","url":null,"abstract":"<div><p>This paper is devoted, first of all, to give a complete unified proof of the characterization theorem for compact generalized Kähler manifolds. The proof is based on the classical duality between “closed” positive forms and “exact” positive currents. In the last part of the paper we approach the general case of non compact complex manifolds, where “exact” positive forms seem to play a more significant role than “closed” forms. In this setting, we state the appropriate characterization theorems and give some interesting applications.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 1","pages":"217 - 245"},"PeriodicalIF":0.4,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0193-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50053399","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
Correction to: Split buildings of type (mathsf {F_4}) in buildings of type (mathsf {E_6}) 修正:在类型的建筑物中拆分类型为(mathsf {F_4})的建筑物 (mathsf {E_6})
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-02-09 DOI: 10.1007/s12188-018-0192-y
Anneleen De Schepper, N. S. Narasimha Sastry, Hendrik Van Maldeghem
{"title":"Correction to: Split buildings of type (mathsf {F_4}) in buildings of type (mathsf {E_6})","authors":"Anneleen De Schepper,&nbsp;N. S. Narasimha Sastry,&nbsp;Hendrik Van Maldeghem","doi":"10.1007/s12188-018-0192-y","DOIUrl":"10.1007/s12188-018-0192-y","url":null,"abstract":"","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 1","pages":"161 - 161"},"PeriodicalIF":0.4,"publicationDate":"2018-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0192-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50034103","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
Asymptotic analysis of expectations of plane partition statistics 平面划分统计量期望的渐近分析
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-02-06 DOI: 10.1007/s12188-018-0191-z
Ljuben Mutafchiev
{"title":"Asymptotic analysis of expectations of plane partition statistics","authors":"Ljuben Mutafchiev","doi":"10.1007/s12188-018-0191-z","DOIUrl":"10.1007/s12188-018-0191-z","url":null,"abstract":"<div><p>Assuming that a plane partition of the positive integer <i>n</i> is chosen uniformly at random from the set of all such partitions, we propose a general asymptotic scheme for the computation of expectations of various plane partition statistics as <i>n</i> becomes large. The generating functions that arise in this study are of the form <i>Q</i>(<i>x</i>)<i>F</i>(<i>x</i>), where <span>(Q(x)=prod _{j=1}^infty (1-x^j)^{-j})</span> is the generating function for the number of plane partitions. We show how asymptotics of such expectations can be obtained directly from the asymptotic expansion of the function <i>F</i>(<i>x</i>) around <span>(x=1)</span>. The representation of a plane partition as a solid diagram of volume <i>n</i> allows interpretations of these statistics in terms of its dimensions and shape. As an application of our main result, we obtain the asymptotic behavior of the expected values of the largest part, the number of columns, the number of rows (that is, the three dimensions of the solid diagram) and the trace (the number of cubes in the wall on the main diagonal of the solid diagram). Our results are similar to those of Grabner et al. (Comb Probab Comput 23:1057–1086, 2014) related to linear integer partition statistics. We base our study on the Hayman’s method for admissible power series.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 1","pages":"255 - 272"},"PeriodicalIF":0.4,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-018-0191-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50010888","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: 3
Split buildings of type (mathsf {F_4}) in buildings of type (mathsf {E_6}) 在类型的建筑物中拆分类型为(mathsf {F_4})的建筑物 (mathsf {E_6})
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2018-01-16 DOI: 10.1007/s12188-017-0190-5
Anneleen De Schepper, N. S. Narasimha Sastry, Hendrik Van Maldeghem
{"title":"Split buildings of type (mathsf {F_4}) in buildings of type (mathsf {E_6})","authors":"Anneleen De Schepper,&nbsp;N. S. Narasimha Sastry,&nbsp;Hendrik Van Maldeghem","doi":"10.1007/s12188-017-0190-5","DOIUrl":"10.1007/s12188-017-0190-5","url":null,"abstract":"<div><p>A symplectic polarity of a building <span>(varDelta )</span> of type <span>(mathsf {E_6})</span> is a polarity whose fixed point structure is a building of type <span>(mathsf {F_4})</span> containing residues isomorphic to symplectic polar spaces (i.e., so-called <i>split buildings</i> of type <span>(mathsf {F_4})</span>). In this paper, we show in a geometric way that every building of type <span>(mathsf {E_6})</span> contains, up to conjugacy, a unique class of symplectic polarities. We also show that the natural point-line geometry of each split building of type <span>(mathsf {F_4})</span> fully embedded in the natural point-line geometry of <span>(varDelta )</span> arises from a symplectic polarity.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 1","pages":"97 - 160"},"PeriodicalIF":0.4,"publicationDate":"2018-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-017-0190-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50032407","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: 3
Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces? 为什么没有一个凸多面体的存在性定理，它的面有规定的方向和周长?
IF 0.4 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2017-12-11 DOI: 10.1007/s12188-017-0189-y
Victor Alexandrov
{"title":"Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces?","authors":"Victor Alexandrov","doi":"10.1007/s12188-017-0189-y","DOIUrl":"10.1007/s12188-017-0189-y","url":null,"abstract":"<div><p>We choose some special unit vectors <span>({mathbf {n}}_1,ldots ,{mathbf {n}}_5)</span> in <span>({mathbb {R}}^3)</span> and denote by <span>({mathscr {L}}subset {mathbb {R}}^5)</span> the set of all points <span>((L_1,ldots ,L_5)in {mathbb {R}}^5)</span> with the following property: there exists a compact convex polytope <span>(Psubset {mathbb {R}}^3)</span> such that the vectors <span>({mathbf {n}}_1,ldots ,{mathbf {n}}_5)</span> (and no other vector) are unit outward normals to the faces of <i>P</i> and the perimeter of the face with the outward normal <span>({mathbf {n}}_k)</span> is equal to <span>(L_k)</span> for all <span>(k=1,ldots ,5)</span>. Our main result reads that <span>({mathscr {L}})</span> is not a locally-analytic set, i.e., we prove that, for some point <span>((L_1,ldots ,L_5)in {mathscr {L}})</span>, it is not possible to find a neighborhood <span>(Usubset {mathbb {R}}^5)</span> and an analytic set <span>(Asubset {mathbb {R}}^5)</span> such that <span>({mathscr {L}}cap U=Acap U)</span>. We interpret this result as an obstacle for finding an existence theorem for a compact convex polytope with prescribed directions and perimeters of the faces.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"88 1","pages":"247 - 254"},"PeriodicalIF":0.4,"publicationDate":"2017-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-017-0189-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50040280","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
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