Differential geometric approach to the deformation of a pair of complex manifolds and Higgs bundles

Takashi Ono

Vol. 330 (2024), No. 2, 283–316

DOI: 10.2140/pjm.2024.330.283

Abstract

Let $X$ be a complex manifold and $(E,𝜃)$ be a Higgs bundle over $X$. We study the deformation of the triple $(X,E,𝜃)$. We introduce the differential graded Lie algebra (DGLA) which governs the deformation. We construct the Kuranishi family of it and prove it contains all the information of small deformations of $(X,E,𝜃)$.

Keywords

deformation of complex structure, Kuranishi space

Mathematical Subject Classification

Primary: 32G08

Secondary: 32G05, 58A14

Milestones

Received: 1 November 2023

Revised: 13 June 2024

Accepted: 1 August 2024

Published: 13 September 2024