Generalized Mukai conjecture for special Fano varieties

Marco Andreatta; Elena Chierici; Gianluca Occhetta

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Generalized Mukai conjecture for special Fano varieties

Marco Andreatta·Elena Chierici·Gianluca Occhetta

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Abstract

Let X be a Fano variety of dimension n, pseudoindex i_X and Picard number ρ_X. A generalization of a conjecture of Mukai says that ρ_X(i_X-1)\le n. We prove that the conjecture holds if: a) X has pseudoindex i_X \ge \frac{n+3}{3} and either has a fiber type extremal contraction or does not have small extremal contractions b) X has dimension five.

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Marco Andreatta, Elena Chierici, Gianluca Occhetta. 2003-09-30. Generalized Mukai conjecture for special Fano varieties. https://arxiv.org/abs/math/0309473

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