  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.

Algebraic Geometry;Commutative Algebra