#### Vol. 7, No. 4, 2013

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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