Mathematische Zeitschrift

, Volume 260, Issue 2, pp 431–449 | Cite as

Galois coverings and endomorphisms of projective varieties

Article

Abstract

We prove that the vector bundle associated to a Galois covering of projective manifolds is ample (resp. nef) under very mild conditions. This results is applied to the study of ramified endomorphisms of Fano manifolds with b 2 = 1. It is conjectured that \({\mathbb{P}}_n\) is the only Fano manifold admitting an endomorphism of degree d ≥ 2, and we verify this conjecture in several cases. An important ingredient is a generalization of a theorem of Andreatta–Wisniewski, characterizing projective space via the existence of an ample subsheaf in the tangent bundle.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Marian Aprodu
    • 1
    • 2
  • Stefan Kebekus
    • 3
  • Thomas Peternell
    • 4
  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  2. 2.Şcoala Normală SuperioarăBucharestRomania
  3. 3.Mathematisches InstitutUniversität zu KölnKolnGermany
  4. 4.Mathematisches InstitutUniversität BayreuthBayreuthGermany

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