On Fano manifolds with an unsplit dominating family of rational curves

Carla Novelli

paper

On Fano manifolds with an unsplit dominating family of rational curves

arXiv:1109.1979

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 $i_{X} > (dim X) /3$ .

arXiv comment11 pages. arXiv admin note: substantial text overlap with arXiv:0905.4388