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Asymptotic linear bounds for the Castelnuovo-Mumford regularity

Author(s): Jürgen Herzog; Lê Tuân Hoa; Ngô Viêt Trung
Journal: Trans. Amer. Math. Soc. 354 (2002), 1793-1809.
MSC (2000): Primary 13D45
Posted: January 10, 2002
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Abstract: We prove asymptotic linear bounds for the Castelnuovo-Mumford regularity of certain filtrations of homogeneous ideals whose Rees algebras need not be Noetherian.

References:

[BEL]
A. Bertram, L. Ein and R. Lazarsfeld, Vanishing theorems, a theorem of Severi, and the equations defining projective varieties, J. Amer. Math. Soc. 4 (1991), no. 3, 587-602. MR 92g:14014
[BH1]
W. Bruns and J. Herzog, Cohen-Macaulay rings, Cambridge Univ. Press, Cambridge, 1993. MR 95h:13020
[BH2]
W. Bruns and J. Herzog, On multigraded resolutions, Math. Proc. Cambridge Phil. Soc. 118 (1995), 245-275. MR 96g:13013
[CTV]
M. Catalisano, N.V. Trung and G. Valla, A sharp bound for the regularity index of fat points in general position, Proc. Amer. Math. Soc. 118 (1993), 717-724. MR 93i:13021
[Ch]
K. A. Chandler, Regularity of the powers of an ideal, Commun. Algebra 25 (1997), 3773-3776. MR 98i:13040
[Cu]
S. D. Cutkosky, Irrational asymptotic behaviour of Castelnuovo-Mumford regularity, J. Reine Angew. Math. 522 (2000), 93-103.

[CEL]
S. D. Cutkosky, L. Ein and R. Lazarsfeld, Positivity and complexity of ideal sheaves, Preprint.

[CHT]
S. D. Cutkosky, J. Herzog and N. V. Trung, Asymptotic behaviour of the Castelnuovo-Mumford regularity, Composition Math. 118 (1999), 243-261.MR 2000f:13037

[ELS]
L. Ein, R. Lazarsfeld and K. Smith, Uniform bounds and symbolic powers on smooth varieties, Invent. Math. 144 (2001), 241-252.

[E]
D. Eisenbud, Commutative algebra, with a view toward algebraic geometry, Springer, 1994. MR 97a:13001
[EG]
D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicities, J. Algebra 88 (1984), 89-133. MR 85f:13023
[GGP]
A. V. Geramita, A. Gimigliano and Y. Pitteloud, Graded Betti numbers of some embedded rational $n$-folds, Math. Ann. 301 (1995), no. 2, 363-380. MR 96f:13022
[GW]
S. Goto and K. Watanabe, On graded rings I, J. Math. Soc. Japan 30 (1978), 179-213. MR 81m:13021
[HH]
M. Hochster and C. Huneke, Comparison of symbolic and ordinary powers of ideals, to appear in Invent. Math.

[HT]
L. T. Hoa and N. V. Trung, On the Castelnuovo-Mumford regularity and the arithmetic degree of monomial ideals, Math. Z. 229 (1998), 519-537. MR 99k:13034
[K]
V. Kodiyalam, Asymptotic behaviour of Castelnuovo-Mumford regularity, Proc. Amer. Math. Soc. 128 (2000), 407-411.MR 2000c:13027
[Mc]
S. McAdam, Asymptotic prime divisions, Lecture Notes in Mathematics 1023, Springer, 1983. MR 85f:13018

[NR]
D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145-158. MR 15:596a
[SS]
K. Smith and I. Swanson, Linear bounds on growth of associated primes, Comm. Algebra 25 (1997), 3071-3079. MR 98k:13003
[St]
B. Sturmfels, Four counterexamples in combinatorial algebraic geometry, J. Algebra 230 (2000), 282-294. MR 2001g:13047
[Sw]
I. Swanson, Powers of ideals. Primary decompositions, Artin-Rees lemma and regularity, Math. Ann. 307 (1997), 299-313. MR 97j:13005
[T1]
N. V. Trung, Reduction exponent and degree bound for the defining equations of graded rings, Proc. Amer. Math. Soc. 101 (1987), 229-236. MR 89i:13031
[T2]
N. V. Trung, The Castelnuovo regularity of the Rees algebra and the associated graded ring, Trans. Amer. Math. Soc. 350 (1998), 2813-2832. MR 98j:13006
[T3]
N. V. Trung, Gröbner bases, local cohomology and reduction number, Proc. Amer. Math. Soc. 129 (2001), 9-18. MR 2001c:13042
[VV]
P. Valabrega and G. Valla, Form rings and regular sequences, Nagoya Math. J. 72 (1978), 93-101. MR 80d:14010
[V]
W. Vasconcelos, Cohomological degrees of graded modules, Six lectures on commutative algebra (Bellaterra, 1996), 345-392, Progr. Math. 166, Birkhäuser, Basel, 1998.MR 99j:13012

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Additional Information:

Jürgen Herzog
Affiliation: Fachbereich Mathematik, Universität-GHS Essen, 45117 Essen, Germany
Email: juergen.herzog@uni-essen.de

Lê Tuân Hoa
Affiliation: Institute of Mathematics, Box 631, Bò Hô, 10000 Hanoi, Vietnam
Email: lthoa@hanimath.ac.vn

Ngô Viêt Trung
Affiliation: Institute of Mathematics, Box 631, Bò Hô, 10000 Hanoi, Vietnam
Email: nvtrung@hn.vnn.vn

DOI: 10.1090/S0002-9947-02-02932-X
PII: S 0002-9947(02)02932-X
Keywords: Castelnuovo-Mumford regularity, reduction number, $a$-invariant, ideal
Received by editor(s): November 25, 2000
Posted: January 10, 2002
Additional Notes: The second and third authors are partially supported by the National Basic Research.
Copyright of article: Copyright 2002, American Mathematical Society

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