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The equations of Rees algebras of equimultiple ideals of deviation one


Authors: Ferran Muiños and Francesc Planas-Vilanova
Journal: Proc. Amer. Math. Soc. 141 (2013), 1241-1254
MSC (2010): Primary 13A30
DOI: https://doi.org/10.1090/S0002-9939-2012-11398-X
Published electronically: September 12, 2012
MathSciNet review: 3008872
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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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Additional Information

Ferran Muiños
Affiliation: Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Diagonal 647, ETSEIB, 08028 Barcelona, Spain
Email: ferranmuinos@gmail.com

Francesc Planas-Vilanova
Affiliation: Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Diagonal 647, ETSEIB, 08028 Barcelona, Spain
Email: francesc.planas@upc.edu

DOI: https://doi.org/10.1090/S0002-9939-2012-11398-X
Keywords: Blowing-up algebras, relation type, reduction number
Received by editor(s): March 16, 2011
Received by editor(s) in revised form: August 22, 2011
Published electronically: September 12, 2012
Additional Notes: The second author is partially supported by the Spanish grant MTM2010-20279.
Communicated by: Irena Peeva
Article copyright: © Copyright 2012 American Mathematical Society

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