# Deformation of Locally Free Sheaves and Hitchin Pairs over Nodal Curve

## TL;DR

This paper investigates the deformation theory of locally free sheaves and Hitchin pairs on nodal curves, linking their deformations to moduli space dimensions and generalized parabolic structures.

## Contribution

It establishes an equivalence between deformations of sheaves and Hitchin pairs on nodal curves and those on their normalizations with parabolic structures.

## Key findings

- Deformation spaces correspond to tangent spaces of moduli spaces.
- Deformation theory relates to generalized parabolic bundles.
- Results facilitate dimension calculations of moduli spaces.

## Abstract

In this article, we study the deformation theory of locally free sheaves and Hitchin pairs over a nodal curve. As a special case, the infinitesimal deformation of these objects gives the tangent space of the corresponding moduli spaces, which can be used to calculate the dimension of the corresponding moduli space. We show that the deformation of locally free sheaves and Hitchin pairs over a nodal curve is equivalent to the deformation of generalized parabolic bundles and generalized parabolic Hitchin pairs over the normalization of the nodal curve respectively.