Bounds on the CastelnuovoMumford regularity of tensor products
Author:
Giulio Caviglia
Journal:
Proc. Amer. Math. Soc. 135 (2007), 19491957
MSC (2000):
Primary 13D45, 13D02
Published electronically:
February 16, 2007
MathSciNet review:
2299466
Fulltext PDF Free Access
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Abstract: In this paper we show how, given a complex of graded modules and knowing some partial CastelnuovoMumford regularities for all the modules in the complex and for all the positive homologies, it is possible to get a bound on the regularity of the zero homology. We use this to prove that if , then , generalizing results of Chandler, Conca and Herzog, and Sidman. Finally we give a description of the regularity of a module in terms of the postulation numbers of filter regular hyperplane restrictions.
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 A. Conca and J. Herzog, CastelnuovoMumford regularity of products of ideals. Collect. Math. 54 (2003), no. 2, 137152. MR 1995137 (2004k:13020)
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 A. Geramita, A. Gimigliano, and Y. Pitteloud, Graded Betti numbers of some embedded rational folds. Math. Ann. 301 (1995), no. 2, 363380. MR 1314592 (96f:13022)
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 D. Mumford, Lectures on curves on an algebraic surface. With a section by G. M. Bergman. Annals of Mathematics Studies, No. 59 Princeton University Press, Princeton, N.J., 1966. xi+200 pp. MR 0209285 (35:187)
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 J. Sidman, On the CastelnuovoMumford regularity of products of ideal sheaves. Adv. Geom. 2 (2002), no. 3, 219229. MR 1924756 (2003f:13021)
 [St]
 B. Sturmfels, Four counterexamples in combinatorial algebraic geometry. J. Algebra 230 (2000), no. 1, 282294. MR 1774768 (2001g:13047)
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Additional Information
Giulio Caviglia
Affiliation:
Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 947203840
Email:
caviglia@math.berkeley.edu
DOI:
http://dx.doi.org/10.1090/S0002993907082226
PII:
S 00029939(07)082226
Keywords:
CastelnuovoMumford regularity,
postulation number,
filterregular sequence
Received by editor(s):
March 3, 2003
Received by editor(s) in revised form:
February 1, 2005
Published electronically:
February 16, 2007
Additional Notes:
The author was partially supported by the “Istituto Nazionale di Alta Matematica Francesco Severi”, Rome
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
