Sur une conjecture de Mukai
Laurent Bonavero
Université Grenoble I, Saint-Martin-d'Hères, FranceStéphane Druel
Université Grenoble I, Saint-Martin-d'Hères, FranceOlivier Debarre
École Normale Supérieure, Paris, FranceCinzia Casagrande
Università di Pisa, Italy

Abstract
Generalizing a question of Mukai, we conjecture that a Fano manifold X with Picard number and pseudo-index satisfies ( - 1) <= dim(X). We prove this inequality in several situations: X is a Fano manifold of dimension <= 4, X is a toric Fano manifold of dimension <= 7 or X is a toric Fano manifold of arbitrary dimension with >= dim(X) / 3 + 1. Finally, we offer a new approach to the general case.
Cite this article
Laurent Bonavero, Stéphane Druel, Olivier Debarre, Cinzia Casagrande, Sur une conjecture de Mukai. Comment. Math. Helv. 78 (2003), no. 3, pp. 601–626
DOI 10.1007/S00014-003-0765-X