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Communications in Number Theory and Physics最新文献

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A rank $2$ Dijkgraaf–Moore–Verlinde–Verlinde formula 秩$2$ Dijkgraaf-Moore-Verlinde-Verlinde公式
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-01-08 DOI: 10.4310/CNTP.2019.V13.N1.A6
L. Gottsche, M. Kool
{"title":"A rank $2$ Dijkgraaf–Moore–Verlinde–Verlinde formula","authors":"L. Gottsche, M. Kool","doi":"10.4310/CNTP.2019.V13.N1.A6","DOIUrl":"https://doi.org/10.4310/CNTP.2019.V13.N1.A6","url":null,"abstract":"We conjecture a formula for the virtual elliptic genera of moduli spaces of rank 2 sheaves on minimal surfaces $S$ of general type. We express our conjecture in terms of the Igusa cusp form $chi_{10}$ and Borcherds type lifts of three quasi-Jacobi forms which are all related to the Weierstrass elliptic function. We also conjecture that the generating function of virtual cobordism classes of these moduli spaces depends only on $chi(mathcal{O}_S)$ and $K_S^2$ via two universal functions, one of which is determined by the cobordism classes of Hilbert schemes of points on $K3$. We present generalizations of these conjectures, e.g. to arbitrary surfaces with $p_g>0$ and $b_1=0$. \u0000We use a result of J. Shen to express the virtual cobordism class in terms of descendent Donaldson invariants. In a prequel we used T. Mochizuki's formula, universality, and toric calculations to compute such Donaldson invariants in the setting of virtual $chi_y$-genera. Similar techniques allow us to verify our new conjectures in many cases.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44256568","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: 19
Rooted tree maps 根树图
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2017-12-04 DOI: 10.4310/cntp.2019.v13.n3.a6
Tatsushi Tanaka
{"title":"Rooted tree maps","authors":"Tatsushi Tanaka","doi":"10.4310/cntp.2019.v13.n3.a6","DOIUrl":"https://doi.org/10.4310/cntp.2019.v13.n3.a6","url":null,"abstract":"Based on Hopf algebra of rooted trees introduced by Connes and Kreimer, we construct a class of linear maps on noncommutative polynomial algebra in two indeterminates, namely rooted tree maps. We also prove that their maps induce a class of relations among multiple zeta values.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2017-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41497772","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: 6
Torelli problem for Calabi–Yau threefolds with GLSM description 带GLSM描述的Calabi-Yau三倍的Torelli问题
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2017-11-28 DOI: 10.4310/cntp.2019.v13.n4.a2
Michał Kapustka, M. Rampazzo
{"title":"Torelli problem for Calabi–Yau threefolds with GLSM description","authors":"Michał Kapustka, M. Rampazzo","doi":"10.4310/cntp.2019.v13.n4.a2","DOIUrl":"https://doi.org/10.4310/cntp.2019.v13.n4.a2","url":null,"abstract":"We construct a gauged linear sigma model with two non-birational K\"alher phases which we prove to be derived equivalent, $mathbb{L}$-equivalent, deformation equivalent and Hodge equivalent. This provides a new counterexample to the birational Torelli problem which admits a simple GLSM interpretation.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2017-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45091097","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: 21
Wrońskian factorizations and Broadhurst–Mellit determinant formulae Wrońskian因式分解和Broadhurst-Mellit行列式公式
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2017-11-06 DOI: 10.4310/CNTP.2018.v12.n2.a5
Yajun Zhou
{"title":"Wrońskian factorizations and Broadhurst–Mellit determinant formulae","authors":"Yajun Zhou","doi":"10.4310/CNTP.2018.v12.n2.a5","DOIUrl":"https://doi.org/10.4310/CNTP.2018.v12.n2.a5","url":null,"abstract":"Drawing on Vanhove's contributions to mixed Hodge structures for Feynman integrals in two-di-men-sion-al quantum field theory, we compute two families of determinants whose entries are Bessel moments. Via explicit factorizations of certain Wronskian determinants, we verify two recent conjectures proposed by Broadhurst and Mellit, concerning determinants of arbitrary sizes. With some extensions to our methods, we also relate two more determinants of Broadhurst--Mellit to the logarithmic Mahler measures of certain polynomials.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"12 1","pages":"355-407"},"PeriodicalIF":1.9,"publicationDate":"2017-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47861249","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: 20
Properties of extremal CFTs with small central charge 具有小中心电荷的极值CFTs的性质
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2017-10-29 DOI: 10.4310/cntp.2020.v14.n3.a6
Francesca Ferrari, Sarah M. Harrison
{"title":"Properties of extremal CFTs with small central charge","authors":"Francesca Ferrari, Sarah M. Harrison","doi":"10.4310/cntp.2020.v14.n3.a6","DOIUrl":"https://doi.org/10.4310/cntp.2020.v14.n3.a6","url":null,"abstract":"We analyze aspects of extant examples of 2d extremal chiral (super)conformal field theories with $cleq 24$. These are theories whose only operators with dimension smaller or equal to $c/24$ are the vacuum and its (super)Virasoro descendents. The prototypical example is the monster CFT, whose famous genus zero property is intimately tied to the Rademacher summability of its twined partition functions, a property which also distinguishes the functions of Mathieu and umbral moonshine. However, there are now several additional known examples of extremal CFTs, all of which have at least $mathcal N=1$ supersymmetry and global symmetry groups connected to sporadic simple groups. We investigate the extent to which such a property, which distinguishes the monster moonshine module from other $c=24$ chiral CFTs, holds for the other known extremal theories. We find that in most cases, the special Rademacher summability property present for monstrous and umbral moonshine does not hold for the other extremal CFTs, with the exception of the Conway module and two $c=12, ~mathcal N=4$ superconformal theories with $M_{11}$ and $M_{22}$ symmetry. This suggests that the connection between extremal CFT, sporadic groups, and mock modular forms transcends strict Rademacher summability criteria.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2017-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46211538","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: 6
Picard–Fuchs operators for octic arrangements, I: The case of orphans Picard-Fuchs算子的octic安排，I:孤儿的情况
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2017-09-27 DOI: 10.4310/CNTP.2019.V13.N1.A1
S. Cynk, D. Straten
{"title":"Picard–Fuchs operators for octic arrangements, I: The case of orphans","authors":"S. Cynk, D. Straten","doi":"10.4310/CNTP.2019.V13.N1.A1","DOIUrl":"https://doi.org/10.4310/CNTP.2019.V13.N1.A1","url":null,"abstract":"We report on $25$ families of projective Calabi-Yau threefolds that do not have a point of maximal unipotent monodromy in their moduli space. The construction is based on an analysis of certain pencils of octic arrangements that were found by C. Meyer. There are seven cases where the Picard-Fuchs operator is of order two and $18$ cases where it is of order four. The birational nature of the Picard-Fuchs operator can be used effectively to distinguish between families whose members have the same Hodge numbers.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2017-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48543149","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
Differential zeros of period integrals and generalized hypergeometric functions 周期积分的微分零与广义超几何函数
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2017-09-03 DOI: 10.4310/CNTP.2018.V12.N4.A1
Jingyue Chen, An Huang, B. Lian, S. Yau
{"title":"Differential zeros of period integrals and generalized hypergeometric functions","authors":"Jingyue Chen, An Huang, B. Lian, S. Yau","doi":"10.4310/CNTP.2018.V12.N4.A1","DOIUrl":"https://doi.org/10.4310/CNTP.2018.V12.N4.A1","url":null,"abstract":"In this paper, we study the zero loci of local systems of the form $deltaPi$, where $Pi$ is the period sheaf of the universal family of CY hypersurfaces in a suitable ambient space $X$, and $delta$ is a given differential operator on the space of sections $V^vee=Gamma(X,K_X^{-1})$. Using earlier results of three of the authors and their collaborators, we give several different descriptions of the zero locus of $deltaPi$. As applications, we prove that the locus is algebraic and in some cases, non-empty. We also give an explicit way to compute the polynomial defining equations of the locus in some cases. This description gives rise to a natural stratification to the zero locus.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"12 1","pages":"609-655"},"PeriodicalIF":1.9,"publicationDate":"2017-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45714889","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: 1
$E_n$ Jacobi forms and Seiberg–Witten curves $E_n$Jacobi形式与Seiberg–Witten曲线
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2017-06-14 DOI: 10.4310/CNTP.2019.v13.n1.a2
K. Sakai
{"title":"$E_n$ Jacobi forms and Seiberg–Witten curves","authors":"K. Sakai","doi":"10.4310/CNTP.2019.v13.n1.a2","DOIUrl":"https://doi.org/10.4310/CNTP.2019.v13.n1.a2","url":null,"abstract":"We discuss Jacobi forms that are invariant under the action of the Weyl group of type E_n (n=6,7,8). For n=6,7 we explicitly construct a full set of generators of the algebra of E_n weak Jacobi forms. We first construct n+1 independent E_n Jacobi forms in terms of Jacobi theta functions and modular forms. By using them we obtain Seiberg-Witten curves of type E_6 and E_7 for the E-string theory. The coefficients of each curve are E_n weak Jacobi forms of particular weights and indices specified by the root system, realizing the generators whose existence was shown some time ago by Wirthm\"uller.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2017-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46868785","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: 17
Specialization of cycles and the $K$-theory elevator 周期的专业化和K理论升降机
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2017-04-16 DOI: 10.4310/CNTP.2019.V13.N2.A2
P. Ángel, C. Doran, J. Iyer, M. Kerr, James D. Lewis, S. Muller-Stach, D. Patel
{"title":"Specialization of cycles and the $K$-theory elevator","authors":"P. Ángel, C. Doran, J. Iyer, M. Kerr, James D. Lewis, S. Muller-Stach, D. Patel","doi":"10.4310/CNTP.2019.V13.N2.A2","DOIUrl":"https://doi.org/10.4310/CNTP.2019.V13.N2.A2","url":null,"abstract":"A general specialization map is constructed for higher Chow groups and used to prove a \"going-up\" theorem for algebraic cycles and their regulators. The results are applied to study the degeneration of the modified diagonal cycle of Gross and Schoen, and of the coordinate symbol on a genus-2 curve.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2017-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48121050","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: 12
Vector bundles and modular forms for Fuchsian groups of genus zero 零亏格Fuchsian群的向量丛和模形式
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2017-04-06 DOI: 10.4310/cntp.2019.v13.n3.a1
L. Candelori, C. Franc
{"title":"Vector bundles and modular forms for Fuchsian groups of genus zero","authors":"L. Candelori, C. Franc","doi":"10.4310/cntp.2019.v13.n3.a1","DOIUrl":"https://doi.org/10.4310/cntp.2019.v13.n3.a1","url":null,"abstract":"This article lays the foundations for the study of modular forms transforming with respect to representations of Fuchsian groups of genus zero. More precisely, we define geometrically weighted graded modules of such modular forms, where the graded structure comes from twisting with all isomorphism classes of line bundles on the corresponding compactified modular curve, and we study their structure by relating it to the structure of vector bundles over orbifold curves of genus zero. We prove that these modules are free whenever the Fuchsian group has at most two elliptic points. For three or more elliptic points, we give explicit constructions of indecomposable vector bundles of rank two over modular orbifold curves, which give rise to non-free modules of geometrically weighted modular forms.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2017-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49638499","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: 9
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