Projective varieties with nef tangent bundle in positive characteristic
Akihiro Kanemitsu, Kiwamu Watanabe

TL;DR
This paper studies smooth projective varieties over fields of positive characteristic with nef tangent bundles, showing they admit special fibrations with Fano fibers and relating their structure to abelian varieties under Frobenius liftability.
Contribution
It proves the existence of smooth fibrations with Fano fibers and flat tangent bundles for such varieties, and links Frobenius liftability to their structure as fibered products over abelian varieties.
Findings
Existence of smooth morphisms with Fano fibers and flat tangent bundles.
Frobenius liftability implies the variety is fibered over an abelian variety.
Varieties are, up to finite cover, fibered over ordinary abelian varieties.
Abstract
Let be a smooth projective variety defined over an algebraically closed field of positive characteristic whose tangent bundle is nef. We prove that admits a smooth morphism such that the fibers are Fano varieties with nef tangent bundle and is numerically flat. We also prove that extremal contractions exist as smooth morphisms. As an application, we prove that, if the Frobenius morphism can be lifted modulo , then admits, up to a finite \'etale Galois cover, a smooth morphism onto an ordinary abelian variety whose fibers are products of projective spaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Vietnamese History and Culture Studies · Commutative Algebra and Its Applications
