Algebraic intermediate hyperbolicities
type: Item
instance of: scholarly article
title: Algebraic intermediate hyperbolicities
author: Antoine Etesse
author: Ariyan Javanpeykar
author: Erwan Rousseau
published in: Documenta Mathematica
publication date: 2023-04-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/2012.07803
review text: Summary: 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.
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 14E07
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14G99
Mathematics Subject Classification ID: 11G35
Mathematics Subject Classification ID: 14G05
zbMATH DE Number: 7671246
zbMATH Keywords: hyperbolicity
zbMATH Keywords: moduli spaces of maps
zbMATH Keywords: ampleness
zbMATH Keywords: positivity
zbMATH Keywords: lang conjectures
MaRDI profile type: Publication
OpenAlex ID: W4388927284
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DOI: 10.25537/DM.2022V27.2469-2490
description: scientific article; zbMATH DE number 7671246