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2013 Adjoint ideals and a correspondence between log canonicity and $F$-purity
Shunsuke Takagi
Algebra Number Theory 7(4): 917-942 (2013). DOI: 10.2140/ant.2013.7.917


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.


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Shunsuke Takagi. "Adjoint ideals and a correspondence between log canonicity and $F$-purity." Algebra Number Theory 7 (4) 917 - 942, 2013.


Received: 1 July 2011; Revised: 23 April 2012; Accepted: 27 May 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1305.14010
MathSciNet: MR3095231
Digital Object Identifier: 10.2140/ant.2013.7.917

Primary: 13A35
Secondary: 14B05 , 14F18

Keywords: $F$-pure singularities , adjoint ideals , log canonical singularities , test ideals

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 4 • 2013
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