## Algebra & Number Theory

### Linear determinantal equations for all projective schemes

#### 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.

#### Article information

Source
Algebra Number Theory, Volume 5, Number 8 (2011), 1041-1061.

Dates
Revised: 31 May 2011
Accepted: 30 June 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513729732

Digital Object Identifier
doi:10.2140/ant.2011.5.1041

Mathematical Reviews number (MathSciNet)
MR2948471

Zentralblatt MATH identifier
1250.14002

#### Citation

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

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