2012/10/31 by Linquan Ma, Ma, Linquan, Wenliang Zhang +1 · 3 citations
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.1210.8402
Let R be a polynomial ring over a field K of arbitrary characteristic and D be the ring of differential operators over R. Inspired by Euler formula for homogeneous polynomials, we introduce a class of graded D-modules, called Eulerian graded D-modules. It is proved that a vast class of D-modules, including all composite of local cohomology modules, HJ0i0(HJ1i1...(HJnin(R))) where J1,...,Jn are homogeneous ideals of R, are Eulerian graded. As an application of our theory, we prove that in all characteristic, these composite of local cohomology modules must be isomorphic to a direct sum of *E(n), the graded injective hull of R/m shifted by n. This answers a question raised in arXiv:1102.5336. An application of our theory of Eulerian graded D-modules to the graded injective hull of R/P, where P is a homogeneous prime ideal of R, is discussed as well.