## The local Gromov-Witten theory of curves

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- by Jim Bryan and Rahul Pandharipande; \break with an appendix by Jim Bryan; Rahul Pandharipande
- J. Amer. Math. Soc.
**21**(2008), 101-136 - DOI: https://doi.org/10.1090/S0894-0347-06-00545-5
- Published electronically: December 6, 2006
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## Abstract:

The local Gromov-Witten theory of curves is solved by localization and degeneration methods. Localization is used for the exact evaluation of basic integrals in the local Gromov-Witten theory of $\mathbb P^1$. A TQFT formalism is defined via degeneration to capture higher genus curves. Together, the results provide a complete and effective solution. The local Gromov-Witten theory of curves is equivalent to the local Donaldson-Thomas theory of curves, the quantum cohomology of the Hilbert scheme points of $\mathbb C^2$, and the orbifold quantum cohomology of the symmetric product of $\mathbb C^2$. The results of the paper provide the local Gromov-Witten calculations required for the proofs of these equivalences.## References

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## Bibliographic Information

**Jim Bryan**- Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada
- ORCID: 0000-0003-2541-5678
- Email: jbryan@math.ubc.ca
**Rahul Pandharipande**- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- MR Author ID: 357813
- Email: rahulp@math.princeton.edu
**C. Faber**- Affiliation: Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden
- Email: faber@math.jhu.edu
**A. Okounkov**- Affiliation: Department of Mathematics, Princeton University, Washington Road Fine Hall, Princeton, NJ 08544
- Email: okounkov@math.princeton.edu
- Received by editor(s): December 5, 2005
- Published electronically: December 6, 2006
- Additional Notes: The first author was partially supported by the NSERC, the Clay Institute, and the Aspen Institute.

The second author was partially supported by the Packard foundation and the NSF - © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc.
**21**(2008), 101-136 - MSC (2000): Primary 14N35
- DOI: https://doi.org/10.1090/S0894-0347-06-00545-5
- MathSciNet review: 2350052