Vol. 12, No. 4, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19, 1 issue

Volume 18, 12 issues

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
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