Graded components of local cohomology modules over invariant rings-II

Abstract

Let $A$ be a regular ring containing a field $K$ of characteristic zero and let $R=A[X_1,\dots ,X_m]$. Consider $R$ as standard graded with $°A=0$ and $°X_i=1$ for all $i$. Let $G$ be a finite subgroup of $G{L}_m(A)$. Let $G$ act linearly on $R$ fixing $A$. Let $S=R^G$. In this paper we present a comprehensive study of graded components of local cohomology modules $H_I^i(S)$ where $I$ is an \emph{arbitrary} homogeneous ideal in $S$. We prove stronger results when $G\subseteq G{L}_m(K)$. Some of our results are new even in the case when $A$ is a field.

Better bounds obtained. A proposition corrected. Many typo's corrected