The equations of Rees algebras of equimultiple ideals of deviation one

Muiños, Ferran; Planas-Vilanova, Francesc

doi:10.1090/S0002-9939-2012-11398-X

The equations of Rees algebras of equimultiple ideals of deviation one
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by Ferran Muiños and Francesc Planas-Vilanova PDF

Proc. Amer. Math. Soc. 141 (2013), 1241-1254 Request permission

Abstract:

We describe the equations of the Rees algebra $\mathbf {R}(I)$ of an equimultiple ideal $I$ of deviation one provided that $I$ has a reduction generated by a regular sequence $x_1,\ldots ,x_s$ such that the initial forms $x_1^*,\ldots ,x_{s-1}^*$ are a regular sequence in the associated graded ring. In particular, we prove that there is a single equation of maximum degree in a minimal generating set of the equations of $\mathbf {R}(I)$, which recovers some previous known results.

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