L-infinity Algebras and Deformations of Holomorphic Maps

TL;DR

This paper develops a framework using L-infinity algebras to study infinitesimal deformations of holomorphic maps between compact complex manifolds, providing explicit algebraic descriptions.

Contribution

It introduces a deformation functor for pairs of DGLA morphisms and explicitly characterizes the controlling algebraic structures using L-infinity algebras.

Findings

Construction of a deformation functor for DGLA pairs

Explicit description of the controlling L-infinity algebra

Application to infinitesimal deformations of holomorphic maps

Abstract

We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity structures, we give an explicit description of the differential graded Lie algebra that controls this problem.