Equations of Rees algebras of ideals in two variables

Abstract

Let I be an ideal of height two in R=k[x_0,x_1] generated by forms of the same degree, and let K be the ideal of defining equations of the Rees algebra of I. Suppose that the second largest column degree in the syzygy matrix of I is e. We give an algorithm for computing the minimal generators of K whose degree is at least e, as well as a simple formula for the bidegrees of these generators. In the case where I is an almost complete intersection, we give a generating set for each graded piece K_(i,*) with i>=e-1.