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

作者：Huneke Craig^*; Mantero Paolo; Mccullough Jason; Seceleanu Alexandra

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143(6): 2365-2377.

DOI：10.1090/s0002-9939-2015-12612-3

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 is not an element of 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.

• 出版日期2015-6