On the Rees algebra of certain codimension two perfect ideals

Details On the Rees algebra of certain codimension two perfect ideals On the Rees algebra of certain codimension two perfect ideals

2001-03-14

arxiv.org/abs/math/0103087v1

Manuscripta Mathematica 107 (2002), 479-501

Mathematics

Commutative Algebra

26 pages

Scientific paper

Let X be a set of smooth points in P^2, and I = \oplus_{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 P^2 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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