Multigraded extended Rees algebras of $m$-primary ideals

Details Multigraded extended Rees algebras of $m$-primary ideals Multigraded extended Rees algebras of $m$-primary ideals

2004-09-07

arxiv.org/abs/math/0409096v1

Mathematics

Commutative Algebra

To appear in Nagoya Mathematical Journal

Scientific paper

In this paper we consider multi-graded extended Rees algebras of zero dimensional ideals which are Cohen-Macaulay (CM) with minimal multiplicity. We show that the minimal multiplicity property can occur only for the ordinary extended Rees algebra and the bigraded extended Rees algebra. For the bigraded extended Rees algebra we find necessary conditions for it to be CM with minimal multiplicity. We also produce bigraded Rees algebras which are Cohen-Macaulay with minimal multiplicity.

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