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

Quang Minh Nguyen

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

Quang Minh Nguyen

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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.

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Quang Minh Nguyen. 2004-11-24. The moduli space of rank-3 vector bundles with trivial determinant over a curve of genus 2 and duality. https://arxiv.org/abs/math/0408318

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