On the Rees algebra of certain codimension two perfect ideals

2001/03/14 by Ha Huy Tai
Mathematics · #math.AC #math.AG #msc:13A30 #msc:14J26 #msc:14E25

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published as Manuscripta Mathematica 107 (2002), 479-501 · 26 pages

arxiv created 2001/03/14 · arxiv updated 2009/11/30

Abstract

Let X be a set of smooth points in P², and I = ⊕_{t >= d} I_t the defining ideal of X. In this paper, we give a set of defining equations for the Rees algebra R(I_d+1) of the ideal generated by I_d+1. This study give information to completely answer questions on the defining ideals of projective embeddings of the blowup of P² along the points in X, which has been studied by many authors. In this paper, we also study the asymptotic behaviour of the Rees algebras R(I_t) of the ideal generated by I_t, as t gets large.

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