Counting generic genus–0 curves on Hirzebruch surfaces

Spielberg, Holger

doi:10.1090/S0002-9939-01-06418-8

Counting generic genus–$0$ curves on Hirzebruch surfaces
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Proc. Amer. Math. Soc. 130 (2002), 1257-1264 Request permission

Abstract:

Hirzebruch surfaces $F_{k}$ 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 spaces. We use this example to explain in detail that the counting argument given by Batyrev for toric manifolds does not work.

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