Vector bundles on genus 2 curves and trivectors

DOI10.14231/AG-2019-016zbMATH Open1427.14069arXiv1605.04459MaRDI QIDQ5204030

Steven V. Sam, Eric Rains

Publication date: 9 December 2019

Published in: Algebraic Geometry (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1605.04459

zbMATH Keywords

vector bundlesmoduli spacesinvariant theorygenus 2 curves

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Vector bundles on curves and their moduli (14H60)

Related Items (4)

Title not available (Why is that?) ⋮ Remarks on ample vector bundles of curve genus two ⋮ Vector bundles and symmetric bilinear forms over curves of genus one and arbitrary index ⋮ A generalization of curve genus for ample vector bundles. II

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