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-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.

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

References in corpus (5)

• Syzygies, multigraded regularity and toric varieties
• Ideals of varieties parameterized by certain symmetric tensors
• Frobenius amplitude and strong vanishing theorems for vector bundles
• Multigraded Castelnuovo-Mumford Regularity
• Geometric syzygies of elliptic normal curves and their secant varieties

Cited by in corpus (4)

• Rank 3 Quadratic Generators of Veronese Embeddings
• Deformation and Unobstructedness of Determinantal Schemes
• Linear syzygies of curves in weighted projective space
• On the rank index of projective curves of almost minimal degree