Hodge structures on analytic moduli of real pluriharmonic bundles

TL;DR

This paper constructs a real analytic moduli stack for pluriharmonic bundles on compact Kähler manifolds, revealing Hodge and quaternionic structures, and extends non-abelian mixed Hodge structures to these moduli spaces.

Contribution

It introduces a new real analytic moduli stack for pluriharmonic bundles and demonstrates how to extend non-abelian mixed Hodge structures over it.

Findings

Construction of the real analytic moduli stack with Hodge and quaternionic structures

Establishment of a map to the de Rham moduli stack with preferred sections

Extension of non-abelian mixed Hodge structures to the pluriharmonic moduli stack

Abstract

We define and construct the real analytic moduli stack of pluriharmonic bundles on a compact Kaehler manifold X, and show how this is equipped with Hodge and quaternionic structures. This stack maps to the de Rham moduli stack, giving rise to preferred sections of the Deligne-Hitchin twistor stack. We then show how the non-abelian mixed Hodge structures on Malcev homotopy types X can be extended to objects over the pluriharmonic moduli stack.