Suppose X is a nonsingular projective scheme, Z a nonsingular closed subscheme of X. Let ˜X be the blowup of X centered at Z, E0 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 δ 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 Np for all t⋙e>0.
Asymptotic Behaviour Exceptional Divisor Projective Scheme Closed Subscheme General Hyperplane
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