Singularities of generic linkage of algebraic varieties

Abstract

Let $Y$ be a generic link of a subvariety $X$ of a nonsingular variety $A$. We give a description of the Grauert-Riemenschneider canonical sheaf of $Y$ in terms of the multiplier ideal sheaves associated to $X$ and use it to study the singularities of $Y$. As the first application, we give a criterion when $Y$ has rational singularities and show that log canonical threshold increases and log canonical pairs are preserved in generic linkage. As another application we give a quick and simple liaison method to generalize the results of de Fernex-Ein and Chardin-Ulrich on the Castelnuovo-Mumford regularity bound for a projective variety.