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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Finiteness of Hilbert functions and bounds for Castelnuovo-Mumford regularity of initial ideals
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by Lê Tuân Hoa PDF
Trans. Amer. Math. Soc. 360 (2008), 4519-4540 Request permission

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.
References
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Additional Information
  • Lê Tuân Hoa
  • Affiliation: Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam
  • Email: lthoa@math.ac.vn
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 4519-4540
  • MSC (2000): Primary 13D45, 13D40, 13P10
  • DOI: https://doi.org/10.1090/S0002-9947-08-04424-3
  • MathSciNet review: 2403695