Characteristic cycles of local cohomology modules of monomial ideals

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 HrI (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 (HrI (R)), where p is any homogeneous prime ideal of R. This allows us to compute the Bass numbers of HrI (R) with respect to any prime ideal and describe its associated primes. 1