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This paper presents three results on F-singularities. First, we give a newproof of Eisenstein's restriction theorem for adjoint ideal sheaves, using thetheory of F-singularities. Second, we show that a conjecture of Musta\c{t}\u{a}and Srinivas implies a conjectural correspondence of F-purity and logcanonicity. Finally, we prove this correspondence when the defining equationsof the variety are very general.

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