Generalized Mukai conjecture for special Fano varieties

2003/09/30 by Marco Andreatta, Andreatta, Marco, Elena Chierici +3 · 1 citation
Mathematics · #14E30 #14J45 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E30 #msc:14J45

paper · pdf · doi:10.48550/arxiv.math/0309473

19 pages

arxiv created 2003/09/30 · arxiv updated 2009/12/01

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)≤ n. We prove that the conjecture holds if: a) X has pseudoindex i_X ≥ (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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