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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Inequalities for Hilbert functions and primary decompositions


Author: A. L. Chistov
Translated by: the author
Original publication: Algebra i Analiz, tom 19 (2007), nomer 6.
Journal: St. Petersburg Math. J. 19 (2008), 975-994
MSC (2000): Primary 12F15, 12F20
DOI: https://doi.org/10.1090/S1061-0022-08-01031-5
Published electronically: August 22, 2008
MathSciNet review: 2411963
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Abstract: Upper bounds are found for the characteristic function of a homogeneous polynomial ideal $ I$; such estimates were previously known only for a radical ideal $ I$. An analog of the first Bertini theorem for primary decompositions is formulated and proved. Also, a new representation for primary ideals and modules is introduced and used, which is convenient from an algorithmic point of view.


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Additional Information

A. L. Chistov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: alch@pdmi.ras.ru

DOI: https://doi.org/10.1090/S1061-0022-08-01031-5
Keywords: Characteristic function of an ideal, first Bertini theorem, Hilbert functions
Received by editor(s): May 10, 2007
Published electronically: August 22, 2008
Dedicated: Dedicated to the centenary of D. K. Faddeev’s birth
Article copyright: © Copyright 2008 American Mathematical Society