Generalized Mukai conjecture for special Fano varieties
Abstract
Let X be a Fano variety of dimension n, pseudoindex iX and Picard number X. A generalization of a conjecture of Mukai says that X(iX-1) n. We prove that the conjecture holds if: a) X has pseudoindex iX n+33 and either has a fiber type extremal contraction or does not have small extremal contractions b) X has dimension five.
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