---
title: The moduli space of rank-3 vector bundles with trivial determinant over a curve of genus 2 and duality
url: https://www.emergentmind.com/papers/0408318
type: paper
arxiv_id: '0408318'
arxiv_url: https://arxiv.org/abs/0408318
published: '2004-08-23'
categories:
- math.AG
---

# The moduli space of rank-3 vector bundles with trivial determinant over a curve of genus 2 and duality

## Abstract

Let SU_X(3) be the moduli space of semi-stable vector bundles of rank 3 and trivial determinant on a curve X of genus 2. It maps onto P^8 and the map is a double cover branched over a sextic hypersurface called the Coble sextic. In the dual P^8 there is a unique cubic hypersurface, the Coble cubic, singular exactly along the abelian surface of degree 1 line bundles on X. We give a new proof that these two hypersurfaces are dual. As an immediate corollary, we derive a Torelli-type result.