## Advanced Studies in Pure Mathematics

### Multiplier ideals via Mather discrepancy

#### Abstract

We define a version of multiplier ideals, the Mather multiplier ideals, on a variety with arbitrary singularities, using the Mather discrepancy and the Jacobian ideal. In this context we prove a relative vanishing theorem, thus obtaining restriction, subadditivity and summation theorems. The Mather multiplier ideals also satisfy a Skoda type result. As an application, we obtain a Briançon-Skoda type formula for the integral closures of ideals on a variety with arbitrary singularities.

#### Article information

Dates
First available in Project Euclid: 4 October 2018

https://projecteuclid.org/ euclid.aspm/1538622702

Digital Object Identifier
doi:10.2969/aspm/07010009

Mathematical Reviews number (MathSciNet)
MR3617776

Zentralblatt MATH identifier
1369.14028

#### Citation

Ein, Lawrence; Ishii, Shihoko; Mustaţă, Mircea. Multiplier ideals via Mather discrepancy. Minimal Models and Extremal Rays (Kyoto, 2011), 9--28, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/07010009. https://projecteuclid.org/euclid.aspm/1538622702