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Counting generic genus-$0$ curves on Hirzebruch surfaces


Author: Holger Spielberg
Journal: Proc. Amer. Math. Soc. 130 (2002), 1257-1264
MSC (1991): Primary 14N35; Secondary 53D45, 14H10, 14M25
Published electronically: December 27, 2001
MathSciNet review: 1879945
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-01-06418-8
Keywords: Hirzebruch surfaces, quantum cohomology, Gromov--Witten invariants, toric manifolds
Received by editor(s): October 6, 2000
Published electronically: December 27, 2001
Communicated by: Mohan Ramachandran
Article copyright: © Copyright 2001 American Mathematical Society