On Strongly $F$-Regular Inversion of Adjunction

Abstract

In this article we give two independent proofs of the positive characteristic analog of the log terminal inversion of adjunction. We show that for a pair $(X,S+B)$ in characteristic $p>0$, if $(S^n,B_{S^n})$ is strongly $F$-regular, then $S$ is normal and $(X,S+B)$ is purely $F$-regular near $S$. We also answer affirmatively an open question about the equality of $F$-Different and Different.

A new proof of the Proposition 3.4 is given as per referee's suggestion and some other minor changes in some lemmas. Comments are welcome

References in corpus (1)

• On the three dimensional minimal model program in positive characteristic

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• On the Adjunction Formula for $3$-folds in characteristic $p>5$
• Inversion of adjunction for $F$-signature
• On the local étale fundamental group of KLT threefold singularities
• Inversion of Adjunction for the minimal exponent
• Irregular threefolds with numerically trivial canonical divisor