Arithmetic Macaulayfication of projective schemes

Details Arithmetic Macaulayfication of projective schemes Arithmetic Macaulayfication of projective schemes

2002-09-13

arxiv.org/abs/math/0209156v1

J. Pure Appl. Alg. 201 (2005), no. 1-3, 49-61.

Mathematics

Commutative Algebra

14 pages

Scientific paper

In this paper, we study arithmetic Macaulayfication of projective schemes and Rees algebras of ideals. We give a necessary and sufficient condition for a nonsingular projective scheme to have an arithmetic Macaulayfication. If the scheme is not necessarily nonsingular, we show that our condition give a sufficient condition for the existence of an arithmetic Macaulayfication. We also study truncated Rees algebra of an ideal. We show that the truncated Rees algebra R_\lambda(I) of an ideal I is alway Cohen-Macaulay for \lambda large enough in some important situations.

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