Abstract
A generalization of S. Mukai's conjecture says that if X is a Fano n-fold with Picard number ρX and pseudo-index iX, then ρX(iX−1)≤n, with equality if and only if X≅(PiX−1)ρX. In this paper, we prove that this conjecture holds if n=6 and either X admits an extremal contraction of fiber type or X admits no small extremal contractions.
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