Blowup of straighteningclosed ideals in ordinal Hodge algebras
Authors:
Winfried Bruns, Aron Simis and Ngô Viêt Trung
Journal:
Trans. Amer. Math. Soc. 326 (1991), 507528
MSC:
Primary 13C05; Secondary 13C13, 13C15, 13H10
MathSciNet review:
1005076
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Abstract: We study a class of ideals in graded ordinal Hodge algebras . 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 which, under certain conditions, is sharp for large. Frequently one observes that . 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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 R. Hartshorne, Cohomological dimension of algebraic varieties, Ann. of Math. 88 (1968), 403450. MR 0232780 (38:1103)
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 M. Hochster and J. Eagon, CohenMacaulay rings, invariant theory and the generic perfection of determinantal loci, Amer. J. Math. 93 (1971), 10201058. MR 0302643 (46:1787)
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 J. Herzog, A. Simis and W. Vasconcelos, On the canonical module of the Rees algebra and the associated graded ring of an ideal, J. Algebra 105 (1987), 285302. MR 873664 (87m:13029)
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 , The arithmetic of normal Rees algebras, preprint.
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 , Powers of ideals generated by weak sequences, J. Algebra 68 (1981), 471509. MR 608547 (82k:13003)
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 C. Huneke, A. Simis and W. Vasconcelos, Reduced normal cones are domains, Contemp. Math. (to appear). MR 999985 (90c:13010)
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 H. Matsumura, Commutative algebra, 2nd ed., Benjamin/Cummings, Reading, Mass., 1980. MR 575344 (82i:13003)
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 D. W. Sharpe, On certain polynomial ideals defined by matrices, Quart. J. Math. Oxford Ser. 15 (1964), 155175. MR 0163927 (29:1226)
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 A. Simis and N. V. Trung, The divisor class group of ordinary and symbolic blowups, Math. Z. 198 (1988), 479491. MR 950579 (89i:13015)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199110050768
PII:
S 00029947(1991)10050768
Keywords:
Ordinal Hodge algebras,
standard monomial,
straighteningclosed ideal,
filtration of powers,
Rees algebra,
associated graded ring,
normal,
CohenMacaulay,
Gorenstein,
divisor class group,
rank,
arithmetical rank,
generic matrix,
virtual maximal minor
Article copyright:
© Copyright 1991
American Mathematical Society
