Projective embeddings of projective schemes blown up at subschemes

Suppose X is a nonsingular projective scheme, Z a nonsingular closed subscheme of X. Let X be the blowup of X centered at 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 X given by divisors . When X satisfies a necessary condition, we give explicit values of d and such that for all e>0 and embeds X as a projectively normal and arithmetically Cohen-Macaulay scheme. We also give a uniform bound for the regularities of the ideal sheaves of these embeddings, and study their asymptotic behaviour as t gets large compared to e. When X is a surface and Z is a 0-dimensional subscheme, we further show that these embeddings possess property N _p for all te>0. Mathematics Subject Classification (2000):14E25, 14M05, 13H10.Dedicated to the sixtieth birthday of Prof. A.V. Geramita