Local Cohomology Modules Supported on Monomial Ideals

Graded Components of Local Cohomology Modules II

“…Recall that A contains a field K of characteristic zero. Consider the monomial ideal [18], or [19,Corollary 3.3]), it follows that…”

“…The modules H i I (R) have natural Z n -graded structures and can be approached using combinatorial techniques. However, there is a dictionary between the D-module and the Z n -graded structure of H i I (R), see [1]. It is well-known that H i I (R) u are finite dimensional k-vector spaces for all u ∈ Z n .…”

“…It is well-known that H i I (R) u are finite dimensional k-vector spaces for all u ∈ Z n . Readers are encouraged to look through the survey article [1] for an highlight of recent progress in studying such H i I (R). Let R = u≥0 R u be a standard graded Noetherian ring, and R + = u>0 R u be its irrelevant ideal.…”

“…(i) they have a structure of Z d -graded modules which allows one to study these modules using combinatorial approach, see [12], [18], [19]. (ii) they have a structure of D-modules, see [1], [4], [3].…”

“…It thus follows that M has finite length. [12], [18], [19]). We now give an alternative proof of this fact.…”