BV operators of the Gerstenhaber algebras of holomorphic polyvector fields on toric varieties
Yang Deng, Wei Hong
TL;DR
This paper investigates the existence of Batalin-Vilkovisky (BV) operators in the Gerstenhaber algebra of holomorphic polyvector fields on smooth compact toric varieties, providing a complete characterization.
Contribution
It establishes a necessary and sufficient condition for the existence of BV operators in these Gerstenhaber algebras on toric varieties.
Findings
Characterization of when BV operators exist on toric varieties
Necessary and sufficient condition for BV operator existence
Advances understanding of algebraic structures on holomorphic polyvector fields
Abstract
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 sufficient condition for the existence of BV operators of the Gerstenhaber algebra of holomorphic polyvector fields on any smooth compact toric variety.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics