The Fano index of a positive-dimensional Fano manifold 
is the largest positive integer 
for which 
in the Picard group
for a line bundle 
.
It measures divisibility of the anticanonical class. The Fano pseudoindex
instead minimizes anticanonical degrees over irreducible rational curves, and need
not equal the index.
For 
, the index and pseudoindex
are both 
. Each rational curve's
anticanonical degree is divisible by the index, so the index is at most the pseudoindex.
