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

Projective embeddings of projective schemes blown up at subschemes