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Published January 1, 2008 | Version Published
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The orbifold quantum cohomology of ℂ²/ℤ₃ and Hurwitz-Hodge integrals

Creators

  • 1. ROR icon University of British Columbia
  • 2. ROR icon California Institute of Technology
  • 3. ROR icon Princeton University

Abstract

Let ℤ₃ act on ℂ² by non-trivial opposite characters. Let X = [ℂ²/ℤ₃] be the orbifold quotient, and let Y be the unique crepant resolution. We show that the equivariant genus 0 Gromov-Witten potentials F^x and F^y are equal after a change of variables—verifying the Crepant Resolution Conjecture for the pair (X,Y). Our computations involve Hodge integrals on trigonal Hurwitz spaces, which are of independent interest. In a self-contained Appendix, we derive closed formulas for these Hurwitz-Hodge integrals.

Copyright and License

© 2008 American Mathematical Society.

Acknowledgement

The authors are grateful to R. Cavalieri, A. Craw, H. Esnault, Y. Jiang, and E. Viehweg for helpful conversations.

Funding

J. Bryan was supported by NSERC, T. Graber was supported by the NSF and the Sloan foundation, and R. Pandharipande was supported by the NSF and the Packard foundation. The research was partially pursued at the AMS summer institute in algebraic geometry in Seattle, the Banff International Research Station, and the Instituto Superior Teecnico in Lisbon.

Additional details

Related works

Is new version of
Discussion Paper: https://arxiv.org/abs/math/0510335 (URL)

Funding

Natural Sciences and Engineering Research Council
National Science Foundation
Alfred P. Sloan Foundation
David and Lucile Packard Foundation

Dates

Submitted
2005-11-30
Available
2007-07-09
Published online

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Caltech groups
Division of Physics, Mathematics and Astronomy (PMA)
Publication Status
Published