Hitchin maps and parabolic Hitchin maps on the moduli spaces of Hitchin sheaves on nodal curves

TL;DR

This paper investigates Hitchin and parabolic Hitchin maps on moduli spaces of Hitchin sheaves over nodal curves, analyzing fibers, correspondences, and stability properties, with applications to parabolic Poincaré sheaves.

Contribution

It provides new insights into the structure of Hitchin maps on nodal curves and establishes stability results for parabolic Poincaré sheaves in the coprime case.

Findings

Analysis of fibers of Hitchin maps on nodal curves

Establishment of BNR correspondences in this setting

Proof of parabolic stability of Poincaré sheaves in the coprime case

Abstract

We study the Hitchin maps on the moduli spaces of Hitchin sheaves and parabolic Hitchin sheaves on a nodal integral curve $Y$. We study their fibres, the BNR correspondences and the relation of the restriction of the Hitchin map with very stable bundles. As an application, in the "coprime" case we prove that the parabolic Poincar\'e sheaf on $U_{par}(n, \xi)\times Y$ is parabolic stable where $U_{par}(n, \xi)$ is a fixed determinant moduli space of parabolic sheaves on $Y$.