The equations of Rees algebras of equimultiple ideals of deviation one

Details The equations of Rees algebras of equimultiple ideals of deviation one The equations of Rees algebras of equimultiple ideals of deviation one

2012-03-20

arxiv.org/abs/1203.4448v1

Mathematics

Commutative Algebra

16 pages; to appear in the Proceedings of the American Mathematical Society

Scientific paper

We describe the equations of the Rees algebra R(I) of an equimultiple ideal I of deviation one, provided that I has a reduction J generated by a regular sequence and such that the initial forms of the elements of this sequence, except possibly the last one, are also a regular sequence in the associated graded ring of I. In particular, we prove that there is a single equation of top degree in a minimal generating set of the ideal of equations of R(I) and we relate this degree to the reduction number, recovering several known results in the context.

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