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 $i_X > (dim X)/3$.
On Fano manifolds with an unsplit dominating family of rational curves
NOVELLI, CARLA
2012-01-01
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 $i_X > (dim X)/3$.
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