Variations of Hodge Structures of Rank Three k-Higgs Bundles and Moduli Spaces of Holomorphic Triples

TL;DR

This paper explores the relationship between moduli spaces of holomorphic triples and rank three k-Higgs bundles, focusing on their cohomology and special embeddings, to deepen understanding of variations of Hodge structures.

Contribution

It extends embeddings from moduli spaces of k-Higgs bundles to those of holomorphic triples, analyzing their cohomology and critical submanifolds.

Findings

Identifies isomorphisms between moduli spaces of triples and critical submanifolds of Higgs bundles.

Extends embeddings to study cohomology of these moduli spaces.

Provides new insights into the structure of variations of Hodge structures.

Abstract

There is an isomorphism between the moduli spaces of $\sigma$-stable holomorphic triples and some of the critical submanifolds of the moduli space of $k$-Higgs bundles of rank three, whose elements $(E,\varphi^k)$ correspond to variations of Hodge structure, VHS. There are special embeddings on the moduli spaces of $k$-Higgs bundles of rank three. The main objective here is to study the cohomology of the critical submanifolds of such moduli spaces, extending those embeddings to moduli spaces of holomorphic triples.