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A combinatorial case of the abelian-nonabelian correspondence

  • K. Taipale
Original Paper

Abstract

The abelian-nonabelian correspondence outlined in (Duke Math J 126:101–136, 2005) gives a broad conjectural relationship between (twisted) Gromov-Witten invariants of related GIT quotients. This paper proves a case of the correspondence explicitly relating genus zero m-pointed Gromov-Witten invariants of Grassmannians Gr(2, n) and products of projective space \({{\mathrm{\mathbb {P}}}}^{n-1} \times {{\mathrm{\mathbb {P}}}}^{n-1}\). Computation of the twisted Gromov-Witten invariants of \({{\mathrm{\mathbb {P}}}}^{n-1} \times {{\mathrm{\mathbb {P}}}}^{n-1}\) via localization is used.

Keywords

Quantum cohomology Gromov-Witten invariant  Enumerative geometry Grassmannian Schubert calculus 

Mathematics Subject Classification

Primary 14N35 14M15 Secondary 55N91 

Notes

Acknowledgments

Thanks to Ionuţ Ciocan-Fontanine, my thesis advisor, who suggested this problem and several more. I also benefited from conversation with Ezra Miller, Alexander Voronov, Igor Pak, and Victor Reiner.

References

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Copyright information

© The Managing Editors 2015

Authors and Affiliations

  1. 1.Vincent HallUniversity of MinnesotaMinneapolisUSA

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