On the canonical bundle formula and effective birationality for Fano varieties in char $p>0$

TL;DR

This paper advances the understanding of Fano varieties in positive characteristic by establishing results on boundedness, a simplified canonical bundle formula, and effective birationality, supporting the BAB conjecture.

Contribution

It introduces a more accessible canonical bundle formula and proves effective birationality for certain weak Fano varieties in characteristic p>0.

Findings

Boundedness is invariant under normalizations.

A simplified canonical bundle formula for Fano fibrations.

Effective birationality for specific weak Fano varieties.

Abstract

In this paper, we give some results on the birational geometry of varieties of Fano type and boundedness problems in positive characteristic, including a result ensuring that boundedness is invariant under normalizations, a canonical bundle formula for fibrations of Fano type which is easier to use, and the effective birationality of certain weak Fano varieties with good singularities, which is predicted by the BAB conjecture.