一个非平凡的Calabi-Yau DG代数

证明例1中的DG代数不仅是Koszul,同调光滑DG代数,而且还是一个Calabi-Yau DG代数.该例子说明一个Calabi-Yau DG代数的同调分次代数不一定具有Calabi-Yau性质,甚至可能不是同调光滑的;另外,该例子还说明一个Calabi-Yau DG代数忘掉微分后得到的分次代数不一定是分次Calabi-Yau代数.     

Modularity of Calabi-Yau varieties and conformal field theory

We study the modularity problem of Calabi-Yau varieties from the conformal field theo- retic point of view.We express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dedekind eta functions,which is hoped to shed light on the modularity questions for higher dimensional Calabi-Yau varieties.     

Landau-Ginzburg/Calabi-Yau Correspondence via Wall-Crossing

Landau-Ginzburg/Calabi-Yau correspondence claims the equivalence between the Gromov-Witten theory and the Fan-Jarvis-Ruan-Witten theory.The authors survey recently developed wall-crossing approach to the Landau-Ginzburg/Calabi-Yau correspondence for a quintic threefold.     

S-内射模及S-内射包络

设R是环.设S是一个左R-模簇,E是左R-模.若对任何N∈S,有Ext_R~1(N,E)=0,则E称为S-内射模.本文证明了若S是Baer模簇,则关于S-内射模的Baer准则成立;若S是完备模簇,则每个模有S-内射包络;若对任何单模N,Ext_R~1(N,E)=0,则E称为极大性内射模;若R是交换环,且对任何挠模N,Ext_R~1(N,E)=0,则E称为正则性内射模.作为应用,证明了每个模有极大性内射包络.也证明了交换环R是SM环当且仅当T/R的正则性内射包e(T/R)是∑-正则性内射模,其中T=T(R)表示R的完全分式环,当且仅当每一GV-无挠的正则性内射模是∑-正则性内射模.     

Note on a Conjecture of Gopakumar-Vafa

We rephrase the Gopakumar-Vafa conjecture on genus zero Gromov-Witten invariants of Calabi-Yau threefolds in terms of the virtual degree of the moduli of pure dimension one stable sheaves and investigate the conjecture for K3 fibred local Calabi-Yau threefolds.     

稳定向量丛模空间中的有理曲线

Fano簇中有理曲线的研究是代数几何的重要课题之一,本文对稳定向量丛模空间中有理曲线研究的现状做一个较全面的总结.     

Beijing Lectures on the Grade Restriction Rule

The authors describe the relationships between categories of B-branes in different phases of the non-Abelian gauged linear sigma model.The relationship is described explicitly for the model proposed by Hori and Tong with non-Abelian gauge group that connects two non-birational Calabi-Yau varieties studied by Rφdland.A grade restriction rule for this model is derived using the hemisphere partition function and it is used to map B-type D-branes between the two Calabi-Yau varieties.     

几类森林匹配多项式的因式分解及匹配等价性分析

通过研究几类图簇匹配多项式的因式分解,证明了这几类图簇的非匹配唯一性,并得到这些图簇匹配等价图的结构特征.     

秩为1的有限维pointed Hopf代数的稳定范畴中的Calabi-Yau对象（英文）

设H是秩为1的有限维pointed Hopf代数.借助于Cibils以及张的结果,本文描述了H的稳定范畴H-mod中的极小、以至所有Calabi-Yau对象.     

DG polynomial algebras and their homological properties

In this paper, we introduce and study differential graded(DG for short) polynomial algebras. In brief, a DG polynomial algebra A is a connected cochain DG algebra such that its underlying graded algebra A~# is a polynomial algebra K[x_1, x_2,..., x_n] with |xi| = 1 for any i ∈ {1, 2,..., n}. We describe all possible differential structures on DG polynomial algebras, compute their DG automorphism groups, study their isomorphism problems, and show that they are all homologically smooth and Gorenstein DG algebras. Furthermore, it is proved that the DG polynomial algebra A is a Calabi-Yau DG algebra when its differential ?_A≠ 0 and the trivial DG polynomial algebra(A, 0) is Calabi-Yau if and only if n is an odd integer.     

图的伴随多项式的因式分解定理及应用

我们通过研究Γ-型图簇的伴随多项式的因式分解,证明了这些图簇的补图的色等价图的结构性质和非色唯一性.     

紧致H-扭广义Calabi-Yau流形中形变的整体典范族

在紧致H-扭广义Calabi-Yau流形得到了一个可以用来检验形变中典范截面是否全纯的式子(?).     

乘积G—凸空间内的GB—优化映象的极大元及其应用（1）

引入和研究了一类新的映拓扑空间到不同广义凸空间的集值映象簇.利用连续单位分解定理和Brouwer不动点定理,在乘积广义凸空间的非紧设置下,对这类集值映象簇证明了极大元存在定理.这些定理改进,统一和推广了近期文献中许多重要结果.     

关于奇异模迹的同余与整除恒等式

Zagier研究发现奇异模的迹是一些权为3/2的模形式的傅里叶系数. 结果进而人们研究发现了这些奇异模在各种条件下的迹公式和同余性质. 近来, Ahlgen利用模形式在Hecke算子作用下的关系式证明了奇异模迹的一个精确关系式. 基于此,我们研究得到了一些关于奇异模的迹和Hurwitz-Kronecker类数有趣的同余和整数恒等式.     

Deformations of complex orbifolds and the period maps

We consider the deformations of complex orbifolds with the underlying smooth structures being fixed.As a corollary,we can prove that the deformations of a Calabi-Yau orbifold is unobstructed by using standard arguments.Then we consider the period map for a family of complex Kahler orbifolds.We prove that the period map is holomorphic,horizontal and consistent with our Kodaira-Spencer map.     

循环差分-微分模上双变元维数多项式的Gr?bner基算法北大核心CSCD

Gr?bner基算法是在计算机辅助设计和机器人学、信息安全等领域广泛应用的重要工具.文章在周梦和Winkler(2008)给出的差分-微分模上Gr?bner基算法和差分-微分维数多项式算法基础上,进一步研究了分别差分部分和微分部分的双变元维数多项式算法.在循环差分-微分模情形,构造和证明了利用差分-微分模上Gr?bner基计算双变元维数多项式的算法.     

对偶扩张代数的分裂挠理论与Generic模

设A是一个有限维代数,R是A的对偶扩张代数.MA是一个A-模.给定一个倾斜R-模M（?）AR,我们知道MA一定是一个倾斜A-模 设（TM（?）AR,FM（?）AR）与（TM,FM）是分别由M（?）AR和MR导出的挠理论.本文讨论挠理论的分裂性以及GenericA-模与GenericR-模之间的关系.     

投影空間和代数簇的联与乘积簇的基性质

1.如果已经知道一代数簇上对代数等价关系来讲的各个维数子簇的基,能否由此决定该代数簇与投影空间的联(cross-join)或者乘积簇的基?这篇短文的目的就是给出上述问题的一个肯定回答。同一类型,但更一般的问题还有待更深入一步的研究。我们大体按照Hodge的用语,不过要指出的是:     

关于一类半环上的格林关系的若干研究

研究了加法半群是带,乘法半群是完全正则半群的半环上的格林关系,给出了˙L∧+D(+L,+R)是同余关系的充分必要条件,证明了由这些同余关系所决定的半环类都是半环簇,并给出了这些半环簇的Mal′cev积分解.     

一类特殊的Koszul Calabi-Yau DG代数

假设一个连通上链DG代数A的基分次代数A~#或者同调分次代数H(A)是由一次元素x,y生成的代数kx,y/(xy+yx).本文证明A是Koszul Calabi-Yau DG代数.