ON THE COMPUTATION OF A-INVARIANTS

Abstract

The a-invariant of a graded Cohen-Macaulay ring is the least degree of a generator of its graded canonical module. We compute the a-invariants of (i) graded algebras with straightening laws on upper semi-modular lattices and (ii) the Stanley-Reisner rings of shellable weighted simplicial complexes. The formulas obtained are applied to rings defined by determinantal and pfaffian ideals.