Vol. 5, No. 8, 2011

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Linear determinantal equations for all projective schemes

Jessica Sidman and Gregory G. Smith

Vol. 5 (2011), No. 8, 1041–1061

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.

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