Vol. 5, No. 8, 2011

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

Volume 18
Issue 12, 2133–2308
Issue 11, 1945–2131
Issue 10, 1767–1943
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

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
Linear determinantal equations for all projective schemes

Jessica Sidman and Gregory G. Smith

Vol. 5 (2011), No. 8, 1041–1061
Abstract

We prove that every projective embedding of a connected scheme determined by the complete linear series of a sufficiently ample line bundle is defined by the 2 × 2 minors of a 1-generic matrix of linear forms. Extending the work of Eisenbud, Koh and Stillman for integral curves, we also provide effective descriptions for such determinantally presented ample line bundles on products of projective spaces, Gorenstein toric varieties, and smooth varieties.

Keywords
determinantally presented, linear free resolution, Castelnuovo–Mumford regularity
Mathematical Subject Classification 2000
Primary: 14A25
Secondary: 14F05, 13D02
Milestones
Received: 20 May 2010
Revised: 31 May 2011
Accepted: 30 June 2011
Published: 5 June 2012
Authors
Jessica Sidman
Department of Mathematics and Statistics
Mount Holyoke College
415A Clapp Lab
South Hadley, MA 01075
United States
http://www.mtholyoke.edu/~jsidman/
Gregory G. Smith
Department of Mathematics and Statistics
Queen’s University
512 Jeffery Hall, University Avenue
Kingston, ON K7L 3N6
Canada
http://www.mast.queensu.ca/~ggsmith/