Geodesic
Algebraic intermediate hyperbolicities
Documenta mathematica, Tome 27 (2022), pp. 2469-2490 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/dm/x34
Classification : 11G35, 14E07, 14G05, 14G99, 14J60, 32Q45
Mots-clés : hyperbolicity, positivity, ampleness, moduli spaces of maps, lang conjectures 
@article{10_4171_dm_x34,
     author = {Antoine Etesse and Ariyan Javanpeykar and Erwan Rousseau},
     title = {Algebraic intermediate hyperbolicities},
     journal = {Documenta mathematica},
     pages = {2469--2490},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x34},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x34/}
}
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Antoine Etesse; Ariyan Javanpeykar; Erwan Rousseau. Algebraic intermediate hyperbolicities. Documenta mathematica, Tome 27 (2022), pp. 2469-2490. doi: 10.4171/dm/x34

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