Vector bundles on genus 2 curves and trivectors

Abstract

Given a complex curve C of genus 2, there is a well-known relationship between the moduli space of rank 3 semistable bundles on C and a cubic hypersurface known as the Coble cubic. Some of the aspects of this is known to be related to the geometric invariant theory of the third exterior power of a 9-dimensional complex vector space. We extend this relationship to arbitrary fields and study some of the connections to invariant theory, which will be studied more in-depth in a followup paper.

19 pages

References in corpus (4)

• Moduli of Abelian varieties, Vinberg theta-groups, and free resolutions
• Vector bundles, dualities, and classical geometry on a curve of genus two
• Alternating trilinear forms on a 9-dimensional space and degenerations of (3,3)-polarized Abelian surfaces
• The Picard group of a coarse moduli space of vector bundles in positive characteristic