Deformations of holomorphic Poisson maps

TL;DR

This paper investigates the deformation theory of holomorphic Poisson maps, extending classical deformation results to the Poisson setting and providing algebraic descriptions of first-order deformations and obstructions.

Contribution

It introduces a framework for studying deformations of holomorphic Poisson maps, including algebraic formulations and identification of first-order deformations and obstructions.

Findings

Identified first-order deformations of Poisson morphisms.

Described obstructions to deformations.

Presented algebraic approach using functors of Artin rings.

Abstract

In this paper, we study deformations of holomorphic Poisson maps which extend Horikawa's series of papers on deformations of holomorphic maps in the context of holomorphic Poisson deformations. In appendices, we present deformations of Poisson morphisms in the language of functors of Artin rings which is the algebraic version of deformations of holomorphic Poisson maps. We identity first-order deformations and obstructions.