Invariant theory of ∧3(9) and genus-2 curves

2017/02/28 by Eric M. Rains, Eric Rains, Steven V Sam +1 · 7 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Bijection #Connection (principal bundle) #Geometric invariant theory #Geometry and complex manifolds #Invariant (physics) #Invariant theory #Vector space #math.AG #msc:14H60 #msc:15A72

paper · pdf · doi:10.2140/ant.2018.12.935

published in Algebra & Number Theory 12(4), 935-957 (Mathematical Sciences Publishers) · 20 pages

openalex created_date 2017/03/03 · arxiv created 2018/01/22 · openalex publication_date 2018/07/11 · arxiv updated 2018/07/25 · openalex updated_date 2026/08/05

Abstract

Previous work established a connection between the geometric invariant theory of the third exterior power of a 9-dimensional complex vector space and the moduli space of genus-2 curves with some additional data. We generalize this connection to arbitrary fields, and describe the arithmetic data needed to get a bijection between both sides of this story.

Citations

• Moduli of Abelian Varieties, Vinberg θ-Groups, and Free Resolutions
• VECTOR BUNDLES, DUALITIES AND CLASSICAL GEOMETRY ON A CURVE OF GENUS TWO
• Enriques' classification of surfaces in char.p, III