Adjoint ideals and a correspondence between log canonicity and F-purity

Takagi, Shunsuke

doi:10.2140/ant.2013.7.917

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Adjoint ideals and a correspondence between log canonicity and $F$-purity

Shunsuke Takagi

Vol. 7 (2013), No. 4, 917–942

DOI: 10.2140/ant.2013.7.917

Abstract

This paper presents three results on $F$ -singularities. First, we give a new proof of Eisenstein’s restriction theorem for adjoint ideal sheaves using the theory of $F$ -singularities. Second, we show that a conjecture of Mustaţă and Srinivas implies a conjectural correspondence of $F$ -purity and log canonicity. Finally, we prove this correspondence when the defining equations of the variety are very general.

Dedicated to Professor Shihoko Ishii on the occasion of her sixtieth birthday

Keywords

adjoint ideals, test ideals, $F$-pure singularities, log canonical singularities

Mathematical Subject Classification 2010

Primary: 13A35

Secondary: 14B05, 14F18

Milestones

Received: 1 July 2011

Revised: 23 April 2012

Accepted: 27 May 2012

Published: 29 August 2013

Authors

Shunsuke Takagi
Graduate School of Mathematical Sciences University of Tokyo 3-8-1 Komaba, Meguro-ku Tokyo 153-8914 Japan
http://www.ms.u-tokyo.ac.jp/~stakagi/

Vol. 7, No. 4, 2013