Generalizations of the restriction theorem for multiplier ideals

Abstract

We present an algebro-geometric perspective on some generalizations, due to S. Takagi, of the restriction theorem for multiplier ideals. The first version of the restriction theorem for multiplier ideals was discovered by Esnault and Viehweg. In a series of papers S. Takagi has discovered generalizations of the restriction theorem and some formulas for multiplier ideals that follow from the restriction theorem. He uses the technique of tight closure and reduction to positive characteristic. We are able to provide an algebro-geometric proof of generalizations of his restriction theorem and his subadditivity theorem. We also prove an adjunction formula for relative canonical divisors of factorizing resolutions of singularities.

17 pages. Submitted

References in corpus (3)

• Invariance of Plurigenera
• Adjoint ideals along closed subvarieties of higher codimension
• On a comparison of minimal log discrepancies in terms of motivic integration

Cited by in corpus (8)

• A survey of test ideals
• Singularities with respect to Mather-Jacobian discrepancies
• Minimizing normalized volumes of valuations
• Adjoint ideals and a correspondence between log canonicity and F-purity
• A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume
• A subadditivity formula for multiplier ideals associated to log pairs
• A vanishing theorem for log canonical pairs after De Fernex-Ein
• Inversion of subadjunction and multiplier ideals