Proceedings of the American Mathematical Society

Author(s): Eero Hyry
Journal: Proc. Amer. Math. Soc. 129 (2001), 1299-1308.
MSC (2000): Primary 13A30; Secondary 13B22, 14B05
Posted: October 24, 2000
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Let

be a local ring and let $I\subset A$ be an ideal of positive height. If $J\subset I$ is a reduction of

, then the coefficient ideal $\mathfrak{a}(I,J)$ is by definition the largest ideal $\mathfrak{a}$ such that $I\mathfrak{a}= J\mathfrak{a}$ . In this article we study the ideal $\mathfrak{a}(I,J)$ when the Rees algebra

is Cohen-Macaulay.

1.: I. M. Aberbach and C. Huneke, A theorem of Briançon-Skoda type for regular local rings containing a field, Proc. Amer. Math. Soc. 124 (1996), 707-713. MR 96f:13039
2.: J. Briançon and H. Skoda, Sur la clôture intégrale d'un idéal de germes de functions holomorphes en un point de ${C}^n$ , C.R. Acad. Sci Paris (A) (1974), 949-951. MR 49:5394
3.: S. Goto and K. Nishida, The Cohen-Macaulay and Gorenstein Rees algebras associated to filtrations, Mem. Amer. Math. Soc. 526 (1994). MR 95b:13001
4.: R. Hartshorne, Residues and duality, Springer Lecture Notes, vol. 20, Springer-Verlag, Berlin-Heidelberg-New York, 1966. MR 36:5145
5.: M. Herrmann, E. Hyry, and T. Korb, On Rees algebras with a Gorenstein Veronese subring, J. Algebra 200 (1998), 279-311. MR 98m:13006
6.: M. Herrmann, S. Ikeda, and U. Orbanz, Equimultiplicity and blowing up, Springer-Verlag, Berlin-Heidelberg-New York, 1988. MR 89g:13012
7.: J. Herzog, A. Simis, and W.V. Vasconcelos, On the canonical module of the Rees algebra and the associated graded ring of an ideal, J. Algebra 105 (1987), 285-302. MR 87m:13029
8.: M. Hochster and C. Huneke, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Am. Math. Soc. 3 (1990), 31-116. MR 91g:13010
9.: E. Hyry, Blow-up algebras and rational singularities, Manus. Math. 98 (1999), 377-390. CMP 2000:03
10.: -, Necessary and sufficient conditions for the Cohen-Macaulayness of the form ring, J. Algebra 212 (1999), 17-27. CMP 99:07
11.: E. Hyry, M. Herrmann, and J. Ribbe, On multi-Rees algebras (with an appendix by N. V. Trung), Math. Ann. 301 (1995), 249-279. MR 96c:13005
12.: M. Johnson and B. Ulrich, Artin-Nagata properties and Cohen-Macaulay associated graded rings, Compositio Math. 103 (1996), 7-29. MR 97f:13006
13.: J. Lipman, Rational singularities, with applications to algebraic surfaces and unique factorization, Publ. Math. Inst. Hautes Etudes Sci. 36 (1969), 195-280. MR 43:1986
14.: -, Desingularization of two-dimensional schemes, Ann. of Math. 107 (1978), 151-207. MR 58:10924
15.: -, Adjoints of ideals in regular local rings, Math. Res. Letters 1 (1994), 739-755. MR 95k:13028
16.: -, Cohen-Macaulayness in graded algebras, Math. Res. Letters 1 (1994), 149-157. MR 95d:13006
17.: J. Lipman and A. Sathaye, Jacobian ideals and a theorem of Briançon-Skoda, Michigan Math. J. 28 (1981), 199-222. MR 83m:13001
18.: J. Lipman and B. Teissier, Pseudo-rational local rings and a theorem of Briançon-Skoda, Michigan Math. J. 28 (1981), 97-116. MR 82f:14004
19.: A. Simis, B. Ulrich, and W. V. Vasconcelos, Cohen-Macaulay Rees algebras and degrees of polynomial relations, Math. Ann. 301 (1995), 421-444. MR 96a:13005
20.: N. V. Trung, D.Q Viêt, and S. Zarzuela, When is the Rees algebra Gorenstein?, J. Algebra 175 (1995), 137-156. MR 96h:13007
21.: W. V. Vasconcelos, Aritmetic of blowup algebras, LMS Lect. Note Ser., vol. 195, Cambridge University Press, Cambridge, 1994. MR 95g:13005
22.: -, Lecture notes on Cohen-Macaulay blowup algebras and their equations, Lecture notes for the Workshop on Commutative Algebra and its Relation to Combinatorics and Computer Algebra in Trieste, 1994.
23.: O. Zariski and P. Samuel, Commutative algebra, vol II, Springer Graduate Texts in Mathematics, vol. 29, Springer-Verlag, Berlin-Heidelberg-New York, 1975. MR 52:10706

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