Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Gromov-Witten invariants for abelian and nonabelian quotients


Authors: Aaron Bertram, Ionut Ciocan-Fontanine and Bumsig Kim
Journal: J. Algebraic Geom. 17 (2008), 275-294
DOI: https://doi.org/10.1090/S1056-3911-07-00456-0
Published electronically: October 1, 2007
MathSciNet review: 2369087
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Abstract | References | Additional Information

Abstract: Conjectural formulas are given expressing the genus zero Gromov-Witten invariants of the quotient of a complex projective manifold $ X$ by a reductive group $ G$ (the nonabelian quotient) in terms of the invariants of the quotient by a maximal torus $ T$ (the abelian quotient). The ``$ J$-function'' version of the formulas is proved when $ X$ is a (generalized) flag manifold.


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Additional Information

Aaron Bertram
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: bertram@math.utah.edu

Ionut Ciocan-Fontanine
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: ciocan@math.umn.edu

Bumsig Kim
Affiliation: School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongnyangni 2-dong, Dongdaemun-gu, Seoul, 130-722, Korea
Email: bumsig@kias.re.kr

DOI: https://doi.org/10.1090/S1056-3911-07-00456-0
Received by editor(s): February 1, 2006
Received by editor(s) in revised form: April 6, 2006
Published electronically: October 1, 2007
Additional Notes: The first two authors were partially supported by NSF grants DMS-0200895 and DMS-0303614, respectively. The third author was supported by KOSEF R01-2004-000-10870-0.

American Mathematical Society