Vol. 7, No. 5, 2013

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Sharp upper bounds for the Betti numbers of a given Hilbert polynomial

Giulio Caviglia and Satoshi Murai

Vol. 7 (2013), No. 5, 1019–1064
Abstract

We show that there exists a saturated graded ideal in a standard graded polynomial ring which has the largest total Betti numbers among all saturated graded ideals for a fixed Hilbert polynomial.

Keywords
graded Betti numbers, Hilbert polynomials
Mathematical Subject Classification 2010
Primary: 13D02
Secondary: 13D40
Milestones
Received: 12 October 2010
Revised: 6 December 2012
Accepted: 6 January 2013
Published: 6 September 2013
Authors
Giulio Caviglia
Department of Mathematics
Purdue University
West Lafayette, IN 47901
United States
Satoshi Murai
Department of Mathematical Science
Yamaguchi University
1677-1 Yoshida
Yamaguchi 753-8512
Japan