Moduli of rank 4 symplectic bundles over a curve of genus 2

TL;DR

This paper studies the moduli space of semistable rank 4 symplectic bundles over a genus 2 curve, constructing a finite cover and exploring related geometric properties.

Contribution

It introduces a generically finite cover of the moduli space using 5-dimensional projective spaces, advancing understanding of its geometric structure.

Findings

Constructed a generically finite cover of the moduli space

Connected the moduli space to families of projective spaces

Outlined applications to vector bundle theory

Abstract

Let X be a complex projective curve which is smooth and irreducible of genus 2. The moduli space M_2 of semistable symplectic vector bundles of rank 4 over X is a variety of dimension 10. After assembling some results on vector bundles of rank 2 and odd degree over X, we construct a generically finite cover of M_2 by a family of 5-dimensional projective spaces, and outline some applications.