  Hirzebruch surfaces provide an excellent example to underline the fact that
in general symplectic manifolds, Gromov-Witten invariants might well count
curves in the boundary components of the moduli space. We use this example to
explain in detail that the counting argument given by Batyrev in "Quantum
cohomology rings of toric manifolds" (Asterisque 218:9-34, 1993) does not work.
