Advanced Studies in Pure Mathematics

Multiplier ideals via Mather discrepancy

Lawrence Ein, Shihoko Ishii, and Mircea Mustaţă

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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

Minimal Models and Extremal Rays (Kyoto, 2011), J. Kollár, O. Fujino, S. Mukai and N. Nakayama, eds. (Tokyo: Mathematical Society of Japan, 2016), 9-28

Received: 6 July 2011
First available in Project Euclid: 4 October 2018

Permanent link to this document euclid.aspm/1538622702

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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.

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