Algebra & Number Theory
- Algebra Number Theory
- Volume 5, Number 8 (2011), 1041-1061.
Linear determinantal equations for all projective schemes
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 minors of a -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.
Algebra Number Theory, Volume 5, Number 8 (2011), 1041-1061.
Received: 20 May 2010
Revised: 31 May 2011
Accepted: 30 June 2011
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14A25: Elementary questions
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 13D02: Syzygies, resolutions, complexes
Sidman, Jessica; Smith, Gregory. Linear determinantal equations for all projective schemes. Algebra Number Theory 5 (2011), no. 8, 1041--1061. doi:10.2140/ant.2011.5.1041. https://projecteuclid.org/euclid.ant/1513729732