Algebraic intermediate hyperbolicities

  • Antoine Etesse

    Institut de Mathématique de Toulouse, Université de Paul Sabatier, 31062 Toulouse, France
  • Ariyan Javanpeykar

    Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55099 Mainz, Germany
  • Erwan Rousseau

    Institut Universitaire de France, Université de Brest, CNRS UMR 6205, Laboratoire de Mathematiques de Bretagne Atlantique, France
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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 this article

Antoine Etesse, Ariyan Javanpeykar, Erwan Rousseau, Algebraic intermediate hyperbolicities. Doc. Math. 27 (2022), pp. 2469–2490

DOI 10.4171/DM/X34