JournalscmhVol. 78, No. 3pp. 601–626

Sur une conjecture de Mukai

  • Laurent Bonavero

    Université Grenoble I, Saint-Martin-d'Hères, France
  • Stéphane Druel

    Université Grenoble I, Saint-Martin-d'Hères, France
  • Olivier Debarre

    École Normale Supérieure, Paris, France
  • Cinzia Casagrande

    Università di Pisa, Italy
Sur une conjecture de Mukai cover
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Abstract

Generalizing a question of Mukai, we conjecture that a Fano manifold X with Picard number ρX\rho_X and pseudo-index ιX\iota_X satisfies ρX\rho_X (ιX\iota_X - 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 ιX\iota_X >= 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