Adjoint line bundles and syzygies of projective varieties

Details Adjoint line bundles and syzygies of projective varieties Adjoint line bundles and syzygies of projective varieties

2005-01-26

arxiv.org/abs/math/0501478v4

Vietnam J. Math. (2007), no. 2

Mathematics

Algebraic Geometry

15 pages; fix a mistake in Lemma 3.5; final version

Scientific paper

Let X be a smooth projective variety and let K be the canonical divisor of X. In this paper, we study embeddings of X given by adjoint line bundles of the form K+L, where L is an ample line bundle. When X is a regular surface (i.e. H^1(X, O_X) = 0), we obtain a numerical criterion for K+L to have property Np. When X is a regular variety of arbitrary dimension, under a mild condition, we give an explicit calculation for the regularity of the ideal sheaves of such embeddings.

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