The Beauville-Narasimhan-Ramanan correspondence for twisted Higgs $V$-bundles and components of parabolic $\text{Sp}(2n,\mathbb{R})$-Higgs moduli Spaces

TL;DR

This paper extends the Beauville-Narasimhan-Ramanan correspondence to parabolic Higgs bundles with singularities and Higgs V-bundles, enabling precise counting of moduli space components for maximal parabolic Sp(2n,R)-Higgs bundles.

Contribution

It introduces a generalized correspondence for parabolic Higgs bundles and applies Bott-Morse techniques to determine the number of components in moduli spaces.

Findings

Exact component count for maximal parabolic Sp(2n,R)-Higgs bundle moduli spaces.

Generalization of classical correspondence to singular and V-bundles.

Application of Bott-Morse theory to Higgs bundle moduli spaces.

Abstract

We generalize the classical Beauville-Narasimhan-Ramanan correspondence to the case of parabolic Higgs bundles with regular singularities and Higgs $V$-bundles. Using this correspondence along with Bott-Morse theoretic techniques we provide an exact component count for moduli spaces of maximal parabolic $\text{Sp}\left( 2n,\mathbb{R} \right)$-Higgs bundles with fixed parabolic structure.