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Counts of maps to grassmannians and intersections on the moduli space of bundles

Alina Marian Yale University Dragos Oprea Stanford University

Differential Geometry mathscidoc:1609.10019

Journal of Differential Geometry, 76, (1), 155-175, 2007
We show that intersection numbers on the moduli space of stable bundles of coprime rank and degree over a smooth complex curve can be recovered as highest-degree asymptotics in formulas of Vafa-Intriligator type. In particular, we explicitly evalu- ate all intersection numbers appearing in the Verlinde formula.Our results are in agreement with previous computations of Wit- ten, Jeffrey-Kirwan and Liu. Moreover, we prove the vanishing of certain intersections on a suitable Quot scheme, which can be interpreted as giving equations between counts of maps to the Grassmannian.
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@inproceedings{alina2007counts,
  title={COUNTS OF MAPS TO GRASSMANNIANS AND INTERSECTIONS ON THE MODULI SPACE OF BUNDLES},
  author={Alina Marian, and Dragos Oprea},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160908200611490516676},
  booktitle={Journal of Differential Geometry},
  volume={76},
  number={1},
  pages={155-175},
  year={2007},
}
Alina Marian, and Dragos Oprea. COUNTS OF MAPS TO GRASSMANNIANS AND INTERSECTIONS ON THE MODULI SPACE OF BUNDLES. 2007. Vol. 76. In Journal of Differential Geometry. pp.155-175. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160908200611490516676.
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