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KRS and Powers of determinantal ideas

Published online by Cambridge University Press:  04 December 2007

WINFRIED BRUNS  and
ALDO CONCA
WINFRIED BRUNS
Affiliation:
Universität Osnabrük, FB Mathematik/Informatik, 49069 Osnabrück, Germany, e-mail: Winfried.Bruns@mathematik.uni-osnabrueck.de
ALDO CONCA
Affiliation:
Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy, e-mail: conca@dima.unige.it
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Abstract

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The goal of this paper is to determine Göbner bases of powers of determinantal ideals and to show that the Rees algebras of (products of) determinantal ideals are normal and Cohen–Macaulay if the characteristic of the base field is non-exceptional. Our main combinatorial result is a generalization of Schensted's Theorem on the Knuth–Robinson–Schensted correspondence.

Keywords

Knuth-Robinson-Schensted correspondencedeterminantal ideaRees algebrainitial algebraCohen-Macaulay ring
Type
Research Article
Information
Compositio Mathematica , Volume 111 , Issue 1 , March 1998 , pp. 111 - 122
Copyright
1998 Kluwer Academic Publishers