Vol. 7, No. 4, 2013

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Adjoint ideals and a correspondence between log canonicity and $F$-purity

Shunsuke Takagi

Vol. 7 (2013), No. 4, 917–942
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/