Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds

2022/09/29 by Chen, Youming
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.14511

Abstract

The purpose of this paper is to study the properties of holomorphic Poisson manifolds (M,π) under the assumption of ∂∂--lemma or ∂_π∂--lemma. Under these assumptions,we show that the Koszul--Brylinski homology can be recovered by the Dolbeault cohomology, and prove that the DGLA (A_M^{\bullet,\bullet},∂,[-,-]_∂π) is formal.Furthermore,we discuss the Maurer--Cartan elements of (A_M^{\bullet,\bullet}[[t]],∂,[-,-]_∂π) which induce the deformations of complex structure of M.

Related

• Holomorphic Poisson Cohomology
• Deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes
• Theorem of existence and completeness for holomorphic Poisson structures
• Holomorphic Koszul-Brylinski homologies of Poisson blow-ups
• Deformations of compact holomorphic Poisson submanifolds