Linear determinantal equations for all projective schemes
Algebraic Geometry
2012-06-12 v4 Commutative Algebra
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-minors of a 1-generic matrix of linear forms. Extending the work of Eisenbud-Koh-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 n-folds.
Cite
@article{arxiv.0910.2424,
title = {Linear determinantal equations for all projective schemes},
author = {Jessica Sidman and Gregory G. Smith},
journal= {arXiv preprint arXiv:0910.2424},
year = {2012}
}
Comments
17 pages; several improvements in the exposition following the referee's suggestions