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Mathematische Zeitschrift

, Volume 246, Issue 1–2, pp 111–124 | Cite as

Projective embeddings of projective schemes blown up at subschemes

  • Huy Tài HàEmail author
Article

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 te>0.

Keywords

Asymptotic Behaviour Exceptional Divisor Projective Scheme Closed Subscheme General Hyperplane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA

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