Mathematische Zeitschrift

, Volume 273, Issue 1–2, pp 485–514 | Cite as

Gauged Gromov–Witten theory for small spheres

  • Eduardo Gonzalez
  • Chris WoodwardEmail author


We relate the genus zero gauged Gromov–Witten invariants of a smooth projective variety for sufficiently small area with equivariant Gromov–Witten invariants. As an application we deduce a gauged version of abelianization for Gromov–Witten invariants in the small area chamber. In the symplectic setting, we prove that any sequence of genus zero symplectic vortices with vanishing area has a subsequence that converges after gauge transformation to a holomorphic map with zero average moment map.


Modulus Space Gauge Transformation Homology Class Witten Invariant Kirwan 
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© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Massachusetts BostonBostonUSA
  2. 2.Mathematics-Hill Center, Rutgers UniversityPiscatawayUSA

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