Vol. 5, No. 1, 2011

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

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

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
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Set-theoretic defining equations of the variety of principal minors of symmetric matrices

Luke Oeding

Vol. 5 (2011), No. 1, 75–109
Abstract

The variety of principal minors of n × n symmetric matrices, denoted Zn, is invariant under the action of a group G GL(2n) isomorphic to SL(2)×n Sn. We describe an irreducible G-module of degree-four polynomials constructed from Cayley’s 2 × 2 × 2 hyperdeterminant and show that it cuts out Zn set-theoretically. This solves the set-theoretic version of a conjecture of Holtz and Sturmfels. Standard techniques from representation theory and geometry are explored and developed for the proof of the conjecture and may be of use for studying similar G-varieties.

Keywords
principal minors, symmetric matrices, hyperdeterminant, G-variety, G-module, representation theory, hyperdeterminantal module, relations among minors, variety of principal minors, determinant
Mathematical Subject Classification 2000
Primary: 14M12
Secondary: 15A69, 15A29, 15A72, 20G05, 13A50, 14L30
Milestones
Received: 25 January 2010
Revised: 1 November 2010
Accepted: 5 December 2010
Published: 22 August 2011

Proposed: David Eisenbud
Authors
Luke Oeding
Dipartimento di Matematica “U. Dini”
Università degli Studi di Firenze
Viale Morgagni 67/A
50134 Firenze, Italy
Department of Mathematics
University of California, Berkeley
970 Evans Hall #3840
Berkeley, CA 94720-3840
United States