On Fano manifolds with an unsplit dominating family of rational curves

Details On Fano manifolds with an unsplit dominating family of rational curves On Fano manifolds with an unsplit dominating family of rational curves

2011-09-09

arxiv.org/abs/1109.1979v1

Mathematics

Algebraic Geometry

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

Scientific paper

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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