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Necessary and Sufficient Conditions for the Cohen–Macaulayness of Blowup Algebras

Published online by Cambridge University Press:  04 December 2007

CLAUDIA POLINI  and
BERND ULRICH
CLAUDIA POLINI
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A.; e-mail: polini@math.msu.edu
BERND ULRICH
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A.; e-mail: ulrich@math.msu.edu
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Abstract

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In this paper we provide a complete characterization for when the Rees algebra and the associated graded ring of a perfect Gorenstein ideal of grade three are Cohen–Macaulay. We also treat the case of second analytic deviation one ideals satisfying some mild assumptions. In another set of results we give criteria for an ideal to be of linear type. Finally, we describe the equations defining the Rees algebras of certain Northcott ideals.

Keywords

Rees algebraassociated graded ringCohen–Macaulaynessreduction number.
Type
Research Article
Information
Compositio Mathematica , Volume 119 , Issue 2 , November 1999 , pp. 185 - 207
Copyright
© 1999 Kluwer Academic Publishers