Linear determinantal equations for all projective schemes

Details Linear determinantal equations for all projective schemes Linear determinantal equations for all projective schemes

2009-10-13

arxiv.org/abs/0910.2424v4

Mathematics

Algebraic Geometry

17 pages; several improvements in the exposition following the referee's suggestions

Scientific paper

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.

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