Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 4 (2013), 917-942.
Adjoint ideals and a correspondence between log canonicity and $F$-purity
This paper presents three results on -singularities. First, we give a new proof of Eisenstein’s restriction theorem for adjoint ideal sheaves using the theory of -singularities. Second, we show that a conjecture of Mustaţă and Srinivas implies a conjectural correspondence of -purity and log canonicity. Finally, we prove this correspondence when the defining equations of the variety are very general.
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
Permanent link to this document
Digital Object Identifier
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
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