Theorem of existence and completeness for holomorphic Poisson structures
Algebraic Geometry
2015-12-31 v2 Differential Geometry
Abstract
In this paper, we define a concept of a family of compact holomorphic Poisson manifolds on the basis of Kodaira-Spencer's deformation theory and deduce the integrability condition. We prove an analogue of their `Theorem of existence for complex analytic structures' under some analytic assumption, and establish an analogue of their `Theorem of completeness for complex analytic structures' in the context of holomorphic Poisson deformations.
Cite
@article{arxiv.1407.2026,
title = {Theorem of existence and completeness for holomorphic Poisson structures},
author = {Chunghoon Kim},
journal= {arXiv preprint arXiv:1407.2026},
year = {2015}
}
Comments
proved theorem of completeness for any dimension, and changed notations for cohomology groups