Communications in Mathematical Physics

, Volume 340, Issue 2, pp 851–864 | Cite as

On the Gromov–Witten/Donaldson–Thomas Correspondence and Ruan’s Conjecture for Calabi–Yau 3-Orbifolds

  • Dustin RossEmail author


For any toric Calabi–Yau 3-orbifold with transverse A-singularities, we prove the Gromov–Witten/Donaldson–Thomas correspondence and Ruan’s crepant resolution conjecture in all genera.


Hilbert Scheme Topological Vertex Crepant Resolution Hodge Integral Crepant Resolution Conjecture 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. AKMV05.
    Aganagic M., Klemm A., Mariño M., Vafa C.: The topological vertex. Commun. Math. Phys. 254(2), 425–478 (2005)zbMATHCrossRefADSGoogle Scholar
  2. BCR13.
    Brini, A., Cavalieri, R., Ross, D.: Crepant resolutions and open strings (2013). arXiv:1309.4438
  3. BCY12.
    Bryan J., Cadman C., Young B.: The orbifold topological vertex. Adv. Math. 229(1), 531–595 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  4. Beh09.
    Behrend K.: Donaldson–Thomas type invariants via microlocal geometry. Ann. Math. (2) 170(3), 1307–1338 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  5. CCIT09.
    Coates T., Corti A., Iritani H., Tseng H.-H.: Computing genus-zero twisted Gromov–Witten invariants. Duke Math. J. 147(3), 377–438 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  6. DF05.
    Diaconescu D.-E., Florea B.: Localization and gluing of topological amplitudes. Commun. Math. Phys. 257, 119 (2005)zbMATHMathSciNetCrossRefADSGoogle Scholar
  7. MNOP06.
    Maulik D., Nekrasov N., Okounkov A., Pandharipande R.: Gromov–Witten theory and Donaldson–Thomas theory. I. Compos. Math. 142(5), 1263–1285 (2006)zbMATHMathSciNetGoogle Scholar
  8. MOOP11.
    Maulik D., Oblomkov A., Okounkov A., Pandharipande R.: Gromov–Witten/Donaldson–Thomas correspondence for toric 3-folds. Invent. Math. 186(2), 435–479 (2011)zbMATHMathSciNetCrossRefADSGoogle Scholar
  9. Ros11.
    Ross D.: Localization and gluing of orbifold amplitudes: the Gromov–Witten orbifold vertex. Trans. Am. Math. Soc. 366(3), 1587–1620 (2014)zbMATHCrossRefGoogle Scholar
  10. Ros14.
    Ross, D.: Donaldson–Thomas theory and resolutions of toric transverse A-singularities (2014, preprint). arXiv:1409.7011 [math]
  11. RZ13.
    Ross D., Zong Z.: The gerby Gopakumar-Mariño-Vafa formula. Geom. Topol. 17(5), 2935–2976 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  12. RZ14.
    Ross, D., Zong, Z.: Two-partition cyclic Hodge integrals and loop Schur functions (2014). arXiv:1401.2217
  13. Zho08.
    Zhou, J.: Crepant resolution conjecture in all genera for type A singularities (2008, preprint). arXiv:0811.2023 [math]
  14. Zon15.
    Zong Z.: Generalized Mariño-Vafa formula and local Gromov–Witten theory of orbi-curves. J. Differ. Geom. 100(1), 161–190 (2015)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

Personalised recommendations