A semiregularity map annihilating obstructions to deforming holomorphic maps

TL;DR

This paper generalizes Bloch's semiregularity map to effectively eliminate obstructions in deforming holomorphic maps between compact Kähler manifolds, advancing understanding of their deformation theory.

Contribution

It introduces a generalized semiregularity map that specifically targets obstructions in the deformation of holomorphic maps with fixed codomain.

Findings

The generalized semiregularity map successfully annihilates obstructions.

Provides a new tool for studying deformations of holomorphic maps.

Enhances the theoretical framework of complex geometry and deformation theory.

Abstract

We study deformations of holomorphic maps of compact, complex, K\"ahler manifolds. In particular, we describe a generalization of Bloch's semiregularity map that annihilates obstructions to deform holomorphic maps with fixed codomain.