We prove that Generalized Mukai Conjecture holds for Fano manifolds $X$ of pseudoindex $i_X \geq (dim X + 3)/3$. We also give different proofs of the conjecture for Fano fourfolds and fivefolds.
Rational curves and bounds on the Picard number of Fano manifolds
NOVELLI, CARLA;
2010
Abstract
We prove that Generalized Mukai Conjecture holds for Fano manifolds $X$ of pseudoindex $i_X \geq (dim X + 3)/3$. We also give different proofs of the conjecture for Fano fourfolds and fivefolds.
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