Algebra & Number Theory

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

Shunsuke Takagi

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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

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

Received: 1 July 2011
Revised: 23 April 2012
Accepted: 27 May 2012
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14F18: Multiplier ideals

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


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.

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