Characteristic Cycles of Local Cohomology Modules of Monomial Ideals

In his paper Lyu G Lyubeznik uses the theory of algebraic D modules to study local cohomology modules He proves in particular that if R is any regular ring containing a eld of characteristic zero and I R is an ideal the local cohomology modules H i I R have the following properties i H m H i I R is injective where m is any maximal ideal of R ii inj dimR H i I R dimRH i I R iii The set of the associated primes of H i I R is nite iv All the Bass numbers of H i I R are nite By using the Frobenius map the same results have been obtained by C Huneke and R Y Sharp HS for regular rings containing a eld of positive characteristic By iv Lyubeznik de nes a new set of numerical invariants for any local ring A containing a eld denoted by p i A Namely let R m k be a regular local ring of dimension n containing k and A a local ring which admits a surjective ring homomorphism R A Set I Ker Then p i A is de ned as the Bass number p m H n i I R dim kExt p R k H n i I R This invariant depends only on A i and p but neither on R nor on Completion does not change p i A so if A contains a eld but it is not necesarily the quotient of a regular local ring then one can de ne p i A p i A where A is the completion of A with respect to the maximal ideal Therefore one can always assume R k x xn with x xn independent variables