On the Boundedness of Globally $F$-split varieties

Liam Stigant

On the Boundedness of Globally $F$-split varieties

Algebraic Geometry 2023-02-07 v2

Authors: Liam Stigant

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.

Keywords

f-split varieties globally f-regular positive characteristic birational boundedness mori fibre spaces fano varieties

Cite

@article{arxiv.2008.08123,
  title  = {On the Boundedness of Globally $F$-split varieties},
  author = {Liam Stigant},
  journal= {arXiv preprint arXiv:2008.08123},
  year   = {2023}
}

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