Rational curves and bounds on the Picard number of Fano manifolds

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

2009-05-27

arxiv.org/abs/0905.4388v2

Mathematics

Algebraic Geometry

Modified the proof of the main theorem and eliminated a statement about the cone of curves. To appear in Geometriae Dedicata

Scientific paper

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

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