Deformations of nonsingular Poisson varieties and Poisson invertible sheaves

TL;DR

This paper explores the deformation theory of nonsingular Poisson varieties and sheaves, extending classical deformation concepts and identifying key obstructions and first-order deformations.

Contribution

It introduces a comprehensive framework for deformations of Poisson structures and invertible sheaves, including simultaneous deformations and Poisson vector bundles.

Findings

Identified first-order deformations of Poisson varieties and sheaves

Characterized obstructions to deformations

Extended classical deformation theory to Poisson contexts

Abstract

In this paper, we study deformations of nonsingular Poisson varieties, deformations of Poisson invertible sheaves and simultaneous deformations of nonsingular Poisson varieties and Poisson invertible sheaves, which extend flat deformation theory of nonsingular varieties and invertible sheaves. In an appendix, we study deformations of Poisson vector bundles. We identify first-order deformations and obstructions.