Characteristic cycles of local cohomology modules of monomial ideals II

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 HIr(R) supported on a squarefree monomial ideal Isubset of or equal toR in terms of the Betti numbers of the Alexander dual ideal Ilogical or. 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 image, where image is any homogeneous prime ideal of R. This allows us to compute the Bass numbers of HIr(R) with respect to any prime ideal and describe its associated primes.