Mathematical Research Letters

Volume 29 (2022)

Number 4

Construction of the moduli space of Higgs bundles using analytic methods

Pages: 1011 – 1048

DOI: https://dx.doi.org/10.4310/MRL.2022.v29.n4.a5

Author

Yue Fan (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

Abstract

It is a folklore theorem that the Kuranishi slice method can be used to construct the moduli space of semistable Higgs bundles on a closed Riemann surface as a complex space. The purpose of this paper is to provide a proof in detail. We also give a direct proof that the moduli space is locally modeled on an affine GIT quotient of a quadratic cone by a complex reductive group.

Received 23 May 2020

Accepted 25 August 2020

Published 23 February 2023