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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Blow-up of straightening-closed ideals in ordinal Hodge algebras

Authors: Winfried Bruns, Aron Simis and Ngô Viêt Trung
Journal: Trans. Amer. Math. Soc. 326 (1991), 507-528
MSC: Primary 13C05; Secondary 13C13, 13C15, 13H10
MathSciNet review: 1005076
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Abstract: We study a class of ideals $ I$ in graded ordinal Hodge algebras $ A$. These ideals are distinguished by the fact that their powers have a canonical standard basis. This leads to Hodge algebra structures on the Rees ring and the associated graded ring. Furthermore, from a natural standard filtration one obtains a depth bound for $ A/{I^n}$ which, under certain conditions, is sharp for $ n$ large. Frequently one observes that $ {I^n}= {I^{(n)}}$. Under suitable hypotheses it is possible to calculate the divisor class group of the Rees algebra. Our main examples are ideals of "virtual" maximal minors and ideals of maximal minors "fixing a submatrix".

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Keywords: Ordinal Hodge algebras, standard monomial, straightening-closed ideal, filtration of powers, Rees algebra, associated graded ring, normal, Cohen-Macaulay, Gorenstein, divisor class group, rank, arithmetical rank, generic matrix, virtual maximal minor
Article copyright: © Copyright 1991 American Mathematical Society

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