Characteristic cycles of local cohomology modules of monomial ideals

We study, by using the theory of algebraic D -modules, the local cohomology modules supported on a monomial ideal I of the local regular ring R=k[[x 1 ,…,x n ]] , where k is a field of characteristic zero. We compute the characteristic cycle of H I r (R) and H m p (H I r (R)) , where m is the maximal ideal of R and I is a squarefree monomial ideal. As a consequence, we can decide when the local cohomology module H I r (R) vanishes and compute the cohomological dimension cd(R,I) in terms of the minimal primary decomposition of the monomial ideal I . We also give a Cohen–Macaulayness criterion for the local ring R/I and compute the Lyubeznik numbers λ p,i (R/I)=dim k Ext R p (k,H I n−i (R)) .