Rational curves and bounds on the Picard number of Fano manifolds

2009/05/27 by Carla Novelli, Novelli, Carla, Gianluca Occhetta +1
Mathematics · #14E30 #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0905.4388

openalex publication_date 2009/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that Generalized Mukai Conjecture holds for Fano manifolds X of pseudoindex i_X ≥ (dim X +3)/3. We also give different proofs of the conjecture for Fano fourfolds and fivefolds.

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