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Gnralisant une question de Mukai, nous conjecturons quune varit de Fano X de nombre de Picard X et de pseudo-indice X vrifie $X (X - 1) dim(X). Nous dmontrons cette conjecture dans plusieurs situations: X est une varit de Fano de dimension 4, X est une varit de Fano torique de dimension 7 ou X est une varit de Fano torique de dimension arbitraire avec $X dim(X) / 3 + 1. Enfin, nous prsentons une approche...
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