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CHARACTERISTIC CYCLES OF LOCAL COHOMOLOGY MODULES OF MONOMIAL IDEALS II
 

Summary: CHARACTERISTIC CYCLES OF LOCAL COHOMOLOGY
MODULES OF MONOMIAL IDEALS II
JOSEP `ALVAREZ MONTANER
Abstract. Let R = k[x1, . . . , xn] be the polynomial ring in n independent
variables, where k is a field of characteristic zero. In this work, we will describe
the multiplicities of the characteristic cycle of the local cohomology modules
Hr
I (R) supported on a squarefree monomial ideal I R in terms of the Betti
numbers of the Alexander dual ideal I. From this description we deduce
a Gorensteinness criterion for the quotient ring R/I. On the other side we
give a formula for the characteristic cycle of the local cohomology modules
Hp
p(Hr
I (R)), where p is any homogeneous prime ideal of R. This allows us
to compute the Bass numbers of Hr
I (R) with respect to any prime ideal and
describe its associated primes.
1. Introduction
Let R = k[x1, . . . , xn] be the polynomial ring in n independent variables, where
k is a field of characteristic zero. In [1] we studied the local cohomology modules

  

Source: Alvarez Montaner, Josep - Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya

 

Collections: Mathematics