On Fano manifolds with an unsplit dominating family of rational curves

2011/09/09 by Carla Novelli, Novelli, Carla
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1109.1979

11 pages. arXiv admin note: substantial text overlap with arXiv:0905.4388

arxiv created 2011/09/09 · arxiv updated 2011/12/25

Abstract

We study Fano manifolds X admitting an unsplit dominating family of rational curves and we prove that the Generalized Mukai Conjecture holds if X has pseudoindex i_X = (dim X)/3 or dimension dim X=6. We also show that this conjecture is true for all Fano manifolds with i_X > (dim X)/3.

Citations

• Rational curves and bounds on the Picard number of Fano manifolds

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