Counting generic genus–$0$ curves on Hirzebruch surfaces
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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.References
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Additional Information
- Holger Spielberg
- Affiliation: Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
- Email: Spielberg@member.ams.org
- Received by editor(s): October 6, 2000
- Published electronically: December 27, 2001
- Communicated by: Mohan Ramachandran
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1257-1264
- MSC (1991): Primary 14N35; Secondary 53D45, 14H10, 14M25
- DOI: https://doi.org/10.1090/S0002-9939-01-06418-8
- MathSciNet review: 1879945