On the Adjunction Formula for $3$-folds in characteristic $p>5$

TL;DR

This paper establishes an adjunction formula for certain 3-folds in characteristic p>5, using a Kawamata-Viehweg vanishing theorem to prove normality of log canonical centers.

Contribution

It proves a relative Kawamata-Viehweg vanishing theorem and applies it to derive the adjunction formula for codimension 2 subvarieties on 3-folds in characteristic p>5.

Findings

Proved a Kawamata-Viehweg vanishing-type theorem for 3-folds in characteristic p>5.

Established the normality of minimal log canonical centers.

Derived the adjunction formula for codimension 2 subvarieties.

Abstract

In this article we prove a relative Kawamata-Viehweg vanishing-type theorem for PLT $3$-folds in characteristic $p>5$. We use this to prove the normality of minimal log canonical centers and the adjunction formula for codimension $2$ subvarieties on $\mathbb{Q}$-factorial $3$-folds in characteristic $p>5$.