Equations of Rees algebras of ideals in two variables

2015/11/12 by Madsen, Jeff
#13A30 (Primary) #13D02 #14E05 #14H50 #14Q05 (Secondary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.04073

Abstract

Let I be an ideal of height two in R=k[x₀,x₁] 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.

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