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Projective embeddings of projective schemes blown up at subschemes

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Abstract.

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 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 N p for all t⋙e>0.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO 65211, USA

    Huy Tài Hà

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  1. Huy Tài Hà
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Correspondence to Huy Tài Hà.

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Mathematics Subject Classification (2000):14E25, 14M05, 13H10.

Dedicated to the sixtieth birthday of Prof. A.V. Geramita

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Hà, H. Projective embeddings of projective schemes blown up at subschemes. Math. Z. 246, 111–124 (2004). https://doi.org/10.1007/s00209-003-0586-z

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