Characteristic cycles of local cohomology modules of monomial ideals

We study, by using the theory of algebraic -modules, the local cohomology modules supported on a monomial ideal I of the local regular ring R=k[[x1,…,xn]], where k is a field of characteristic zero. We compute the characteristic cycle of HIr(R) and Hmp(HIr(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 HIr(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 λp,i(R/I)=dimkExtRp(k,HIn−i(R)).