The Fano pseudoindex of a positive-dimensional Fano manifold is the least anticanonical degree of an irreducible rational curve,
 |
Rational curves exist on a Fano manifold, so this minimum is defined. For projective
space 
with 
,
it is 
,
realized by a line. For a product space of positive-dimensional
projective spaces, it is one more than the smallest
factor dimension.
The generalized Mukai conjecture relates the pseudoindex to dimension and Picard
number. Its equality case has all factor dimensions
equal to 
.
