On the Boundedness of Globally $F$-split varieties

DOI10.1007/S00209-023-03236-3zbMATH Open1525.14062arXiv2008.08123MaRDI QIDQ6347324

Publication date: 18 August 2020

Abstract: This paper proposes the use of

F

-split and globally

F

-regular conditions in the pursuit of BAB type results in positive characteristic. The main technical work comes in the form of a detailed study of threefold Mori fibre spaces over positive dimensional bases. As a consequence we prove the main theorem, which reduces birational boundedness for a large class of varieties to the study of prime Fano varieties.

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) (3)-folds (14J30) Minimal model program (Mori theory, extremal rays) (14E30) Positive characteristic ground fields in algebraic geometry (14G17) Rationally connected varieties (14M22)

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