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A MULTIPLICITY BOUND FOR GRADED RINGS AND A CRITERION FOR THE COHEN-MACAULAY PROPERTY.

Authors :
HUNEKE, CRAIG
MANTERO, PAOLO
MCCULLOUGH, JASON
SECELEANU, ALEXANDRA
Source :
Proceedings of the American Mathematical Society; Jun2015, Vol. 143 Issue 6, p2365-2377, 13p
Publication Year :
2015

Abstract

Let R be a polynomial ring over a field. We prove an upper bound for the multiplicity of R/I when I is a homogeneous ideal of the form I = J+(F), where J is a Cohen-Macaulay ideal and F ∉ J. The bound is given in terms of two invariants of R/J and the degree of F. We show that ideals achieving this upper bound have high depth, and provide a purely numerical criterion for the Cohen-Macaulay property. Applications to quasi-Gorenstein rings and almost complete intersections are given. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00029939
Volume :
143
Issue :
6
Database :
Complementary Index
Journal :
Proceedings of the American Mathematical Society
Publication Type :
Academic Journal
Accession number :
101809355
Full Text :
https://doi.org/10.1090/S0002-9939-2015-12612-3