The paper establishes a canonical bundle formula for Fano-type threefold fibrations in large characteristic and proves effective birationality for strongly F-regular weak Fano varieties with bounded Gorenstein index.
Boundedness of weak Fano threefolds with fixed Gorenstein index in positive characteristic
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abstract
In this paper, we give a partial affirmative answer to the BAB conjecture for $3$-folds in characteristic $p>5$. Specifically, we prove that a set $\mathcal{D}$ of weak Fano $3$-folds over an uncountable algebraically closed field is bounded, if each element $X \in \mathcal{D}$ satisfies certain conditions regarding the Gorenstein index, a complement and Kodaira type vanishing. In the course of the proof, we also study a uniform lower bound for Seshadri constants of nef and big invertible sheaves on projective $3$-folds.
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On the canonical bundle formula and effective birationality for Fano varieties in char $p>0$
The paper establishes a canonical bundle formula for Fano-type threefold fibrations in large characteristic and proves effective birationality for strongly F-regular weak Fano varieties with bounded Gorenstein index.