## Algebra & Number Theory

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

Shunsuke Takagi

#### 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.

#### Article information

Source
Algebra Number Theory, Volume 7, Number 4 (2013), 917-942.

Dates
Revised: 23 April 2012
Accepted: 27 May 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513729986

Digital Object Identifier
doi:10.2140/ant.2013.7.917

Mathematical Reviews number (MathSciNet)
MR3095231

Zentralblatt MATH identifier
1305.14010

#### Citation

Takagi, Shunsuke. Adjoint ideals and a correspondence between log canonicity and $F$-purity. Algebra Number Theory 7 (2013), no. 4, 917--942. doi:10.2140/ant.2013.7.917. https://projecteuclid.org/euclid.ant/1513729986

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