A Combinatorial Case of the Abelian-Nonabelian Correspondence

Kaisa Taipale

A Combinatorial Case of the Abelian-Nonabelian Correspondence

Algebraic Geometry 2011-01-11 v1

Authors: Kaisa Taipale

Abstract

The abelian-nonabelian correspondence outlined by Bertram, Ciocan-Fontanine, and Kim 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 $\PP^{n-1} \times \PP^{n-1}$ . Localization is used to compute twisted Gromov-Witten invariants of $\PP^{n-1} \times \PP^{n-1}$ , and comparison of the moduli spaces of stable maps completes the proof.

Keywords

abelian-nonabelian correspondence Gromov-Witten invariants Grassmannian GIT quotient localization stable maps

Cite

@article{arxiv.1101.1548,
  title  = {A Combinatorial Case of the Abelian-Nonabelian Correspondence},
  author = {Kaisa Taipale},
  journal= {arXiv preprint arXiv:1101.1548},
  year   = {2011}
}

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15 pages, 2 figures

A Combinatorial Case of the Abelian-Nonabelian Correspondence

Abstract

Keywords

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