Bound on the a-invariant and reduction numbers of ideals

Clare D'Cruz, Vijay Kodiyalam, Jugal. K. Verma

Let $R$ be a $d$-dimensional standard graded ring over an Artin local ring. Let $M$ be the unique maximal homogeneous ideal of $R.$ Let $h^i(R{)}_n$ denote the length of $H_M^i(R{)}_n$…