论文标题
多贝尔特复合物的形式和全态泊松歧管的变形
Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds
论文作者
论文摘要
本文的目的是在假设$ \ partial _ {} \ bar {\ partial} $ - lemma或$ \partial_π\ bar {\ partial} $ - lemma的假设下研究Holomorphic Poisson歧管$（m，π）$的特性。在这些假设下，我们表明，Koszul-brylinski同源性可以通过Dolbeault Somology恢复，并证明DGLA $（a_m^{\ bullet，\ bullet，\ bullet}，\ bar {\ bar {\ partial} $（a_m^{\ bullet，\ bullet} [[t]]，\ bar {\ partial}，[ - ， - ] _ {\partial_π}）$
The purpose of this paper is to study the properties of holomorphic Poisson manifolds $(M,π)$ under the assumption of $\partial_{}\bar{\partial}$--lemma or $\partial_π\bar{\partial}$--lemma. Under these assumptions,we show that the Koszul--Brylinski homology can be recovered by the Dolbeault cohomology, and prove that the DGLA $(A_M^{\bullet,\bullet},\bar{\partial},[-,-]_{\partial_π})$ is formal.Furthermore,we discuss the Maurer--Cartan elements of $(A_M^{\bullet,\bullet}[[t]],\bar{\partial},[-,-]_{\partial_π})$ which induce the deformations of complex structure of $M$.
