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On coverings of simple abelian varieties

Olivier Debarre (2006)

Bulletin de la Société Mathématique de France

To any finite covering f : Y X of degree d between smooth complex projective manifolds, one associates a vector bundle E f of rank d - 1 on X whose total space contains Y . It is known that E f is ample when X is a projective space ([Lazarsfeld 1980]), a Grassmannian ([Manivel 1997]), or a Lagrangian Grassmannian ([Kim Maniel 1999]). We show an analogous result when X is a simple abelian variety and f does not factor through any nontrivial isogeny X ' X . This result is obtained by showing that E f is M -regular in the...

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