Adjoint ideals along closed subvarieties of higher codimension

Abstract

In this paper, we introduce a notion of adjoint ideal sheaves along closed subvarieties of higher codimension and study its local properties using char- acteristic p methods. When X is a normal Gorenstein closed subvariety of a smooth complex variety A, we formulate a restriction property of the adjoint ideal sheaf adj X (A) of A along X involving the l.c.i. ideal sheaf DX of X. The proof relies on a modification of generalized test ideals of Hara and Yoshida (11).