Geodesic
Algebraic intermediate hyperbolicities
Documenta mathematica, Tome 27 (2022), pp. 2469-2490.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 32Q45, 14E07, 14J60, 14G99, 11G35, 14G05
Keywords: hyperbolicity, moduli spaces of maps, ampleness, positivity, lang conjectures 
@article{DOCMA_2022__27__a5,
     author = {Etesse, Antoine and Javanpeykar, Ariyan and Rousseau, Erwan},
     title = {Algebraic intermediate hyperbolicities},
     journal = {Documenta mathematica},
     pages = {2469--2490},
     publisher = {mathdoc},
     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a5/}
}
TY  - JOUR
AU  - Etesse, Antoine
AU  - Javanpeykar, Ariyan
AU  - Rousseau, Erwan
TI  - Algebraic intermediate hyperbolicities
JO  - Documenta mathematica
PY  - 2022
SP  - 2469
EP  - 2490
VL  - 27
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a5/
LA  - en
ID  - DOCMA_2022__27__a5
ER  - 
%0 Journal Article
%A Etesse, Antoine
%A Javanpeykar, Ariyan
%A Rousseau, Erwan
%T Algebraic intermediate hyperbolicities
%J Documenta mathematica
%D 2022
%P 2469-2490
%V 27
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a5/
%G en
%F DOCMA_2022__27__a5
Etesse, Antoine; Javanpeykar, Ariyan; Rousseau, Erwan. Algebraic intermediate hyperbolicities. Documenta mathematica, Tome 27 (2022), pp. 2469-2490. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a5/