On Burch’s inequality and a reduction system of a filtration

Abstract

Abstract. Let F = {F n } be a multiplicative filtration of a local ring such that the Rees algebra R(F ) is Noetherian. We recall Burch's inequality for F and give an upper bound of the a-invariant of the associated graded ring a(G(F )) using a reduction system of F . Applying those results, we study the symbolic Rees algebra of certain ideals of dimension 2.