Algebraic intermediate hyperbolicities
Abstract
We extend Lang's conjectures to the setting of intermediate hyperbolicity and prove two new results motivated by these conjectures. More precisely, we first extend the notion of algebraic hyperbolicity (originally introduced by Demailly) to the setting of intermediate hyperbolicity and show that this property holds if the appropriate exterior power of the cotangent bundle is ample. Then, we prove that this intermediate algebraic hyperbolicity implies the finiteness of the group of birational automorphisms and of the set of surjective maps from a given projective variety. Our work answers the algebraic analogue of a question of Kobayashi on analytic hyperbolicity.
Cite
@article{arxiv.2012.07803,
title = {Algebraic intermediate hyperbolicities},
author = {Antoine Etesse and Ariyan Javanpeykar and Erwan Rousseau},
journal= {arXiv preprint arXiv:2012.07803},
year = {2021}
}
Comments
14 pages. Comments welcome. Introduction rewritten. Paper structure reordered. Proof of Theorem 0.5 improved