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Finiteness of Hilbert functions and bounds for Castelnuovo-Mumford regularity of initial ideals

Author: Lê Tuân Hoa
Journal: Trans. Amer. Math. Soc. 360 (2008), 4519-4540
MSC (2000): Primary 13D45, 13D40, 13P10
Published electronically: April 4, 2008
MathSciNet review: 2403695
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Abstract: Bounds for the Castelnuovo-Mumford regularity and Hilbert coefficients are given in terms of the arithmetic degree (if the ring is reduced) or in terms of the defining degrees. From this it follows that there exists only a finite number of Hilbert functions associated with reduced algebras over an algebraically closed field with a given arithmetic degree and dimension. A good bound is also given for the Castelnuovo-Mumford regularity of initial ideals which depends neither on term orders nor on the coordinates and holds for any field.

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Additional Information

Lê Tuân Hoa
Affiliation: Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam

Keywords: Castelnuovo-Mumford regularity, local cohomology, Hilbert function, Hilbert polynomial, initial ideal.
Received by editor(s): July 13, 2005
Published electronically: April 4, 2008
Additional Notes: The author was supported in part by the National Basic Research Program (Vietnam). The final preparation of the article was done during his stay at the Centre de Recerca Matematica (Spain).
Dedicated: Dedicated to Professor J. Herzog on the occasion of his 65th birthday
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.