Projective embeddings of projective schemes blown up at subschemes

Details Projective embeddings of projective schemes blown up at subschemes Projective embeddings of projective schemes blown up at subschemes

2002-04-19

arxiv.org/abs/math/0204250v3

Math. Z. 246 (2004), no. 1-2, 111--124.

Mathematics

Algebraic Geometry

14 pages

Scientific paper

Let X be a nonsingular arithmetically Cohen-Macaulay projective scheme, Z a nonsingular subscheme of X. Let \pi: Y --> X be the blowup of X along the ideal sheaf of Z, E_0 the pull-back of a general hyperplane in X and E the exceptional divisor. In this paper, we study projective embeddings of Y given by the divisor tE_0 - eE. We give explicit values of d and \delta such that for all e > 0 and t > ed + \delta, these embeddings is projectively normal and arithmetically Cohen-Macaulay. We also study the regularity of the ideal sheaf and syzygies of these embeddings. When X is a surface and Z is a 0-dimensional subscheme of X, we show that these embeddings possess N_p property for t >> e.

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