Vol. 12, No. 4, 2018

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Invariant theory of $\bigwedge^3(9)$ and genus-2 curves

Eric M. Rains and Steven V Sam

Vol. 12 (2018), No. 4, 935–957
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.

Keywords
genus-2 curves, invariant theory, abelian surfaces, Selmer groups
Mathematical Subject Classification 2010
Primary: 15A72
Secondary: 14H60, 14K05
Milestones
Received: 22 February 2017
Revised: 30 October 2017
Accepted: 16 November 2017
Published: 11 July 2018
Authors
Eric M. Rains
Department of Mathematics 253-37
California Institute of Technology
Pasadena, CA
United States
Steven V Sam
Mathematics Department
University of Wisconsin
Madison, WI
United States