Vector bundles on genus 2 curves and trivectors

2016/05/31 by Eric M. Rains, Steven V Sam
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Biology #Combinatorics #Genus #Geometry and complex manifolds #Hypersurface #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Moduli space #Pure mathematics #Rank (graph theory) #Vector bundle #Zoology #math.AG #msc:14H60 #msc:15A72

paper · pdf · doi:10.14231/ag-2019-016

published as Algebr. Geom. 6 (2019), no. 3, 328-345 · 19 pages

openalex created_date 2016/06/24 · arxiv created 2018/01/22 · openalex publication_date 2019/03/30 · arxiv updated 2019/07/30 · openalex updated_date 2026/08/05

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 are 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.

Citations

• Projectively Dual Varieties
• Generalized theta linear series on moduli spaces of vector bundles on curves
• Moduli of Abelian Varieties, Vinberg θ-Groups, and Free Resolutions
• VECTOR BUNDLES, DUALITIES AND CLASSICAL GEOMETRY ON A CURVE OF GENUS TWO
• The Geometry of Moduli Spaces of Sheaves