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Counting generic genus-0 curves on Hirzebruch surfaces

2000/09/18 by Holger Spielberg, Spielberg, Holger
Mathematics · #14H10 #14M #14N35 #53D45 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.SG #msc:14H10 #msc:14M #msc:14N35 #msc:53D45

paper · pdf · doi:10.48550/arxiv.math/0009169

8 pages, LaTeX

arxiv created 2000/09/18 · openalex publication_date 2000/09/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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