Sur une conjecture de Mukai

• Autores: Laurent Bonavero, Cinzia Casagrande, Olivier Debarre, Stéphane Druel
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 78, Nº 3, 2003, págs. 601-626
• Idioma: francés
• DOI: 10.1007/s00014-003-0765-x
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• Resumen

  • Generalizing a question of Mukai, we conjecture that a Fano manifold X with Picard number $\rho_X$ and pseudo-index $\iota_X$ satisfies $\rho_X$ ($\iota_X$ - 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 $\iota_X$ >= dim(X) / 3 + 1. Finally, we offer a new approach to the general case