Lyubeznik and Betti numbers for homogeneous ideals

Abstract

Let $R=K\left[x_1,\dots ,x_n\right]$ be the standard graded polynomial ring over a field $K$. We’ll study the Lyubeznik numbers of two homogeneous ideals of $R$ whose initial ideals are linked for some monomial order over $R$. We’ll also investigate some relations between Lyubeznik and Betti numbers of homogeneous ideals.