环簇上的全纯多向量场构成的Gerstenhaber代数的BV算子  

BV Operators of the Gerstenhaber Algebras of Holomorphic Polyvector Fields on Toric Varieties

作　　者：邓洋 洪伟 DENG Yang;HONG Wei(School of Mathematics and Statistics,Wuhan University,Wuhan,Hubei,430072,P.R.China;Hubei Key Laboratory of Computational Science,Wuhan,Hubei,430072,P.R.China)

机构地区：[1]武汉大学数学与统计学院,武汉湖北430072 [2]计算科学湖北省重点实验室,武汉湖北430072

出　　处：《数学进展》2023年第2期273-289,共17页Advances in Mathematics（China）

基　　金：Hong is partially supported by NSFC(Nos.12071241,12071358)。

摘　　要：复流形上全纯多向量场构成的线性空间有一个自然的Gerstenhaber代数结构.本文研究紧光滑环簇上全纯多向量场构成的Gerstenhaber代数上的BV算子,给出了该情形下BV算子存在的一个充要条件.The vector space of holomorphic polyvector fields on any complex manifold has a natural Gerstenhaber algebra structure.In this paper,we study BV operators of the Gerstenhaber algebras of holomorphic polyvector fields on smooth compact toric varieties.We give a necessary and suficient condition for the existence of BV operators of the Gerstenhaber algebra of holomorphic polyvector fields on any smooth compact toric variety.

关 键 词：环簇 全纯多向量场 Gerstenhaber代数 BV算子 

分 类 号：O187.2[理学—数学]