The Michigan Mathematical Journal

On computations of genus zero two-point descendant Gromov-Witten invariants

Amin Gholampour and Hsian-Hua Tseng

Full-text: Open access

Article information

Michigan Math. J., Volume 62, Issue 4 (2013), 753-768.

First available in Project Euclid: 16 December 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35] 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]


Gholampour, Amin; Tseng, Hsian-Hua. On computations of genus zero two-point descendant Gromov-Witten invariants. Michigan Math. J. 62 (2013), no. 4, 753--768. doi:10.1307/mmj/1387226163.

Export citation


  • D. Abramovich, T. Graber, and A. Vistoli, Gromov–Witten theory of Deligne–Mumford stacks, Amer. J. Math. 130 (2008), 1337–1398.
  • T. Coates, A. Corti, H. Iritani, and H.-H. Tseng, Quantum cohomology of toric stacks (in preparation).
  • T. Coates, A. Corti, Y.-P. Lee, and H.-H. Tseng, The quantum orbifold cohomology of weighted projective spaces, Acta Math. 202 (2009), 139–193.
  • T. Coates and A. Givental, Quantum Riemann–Roch, Lefschetz, and Serre, Ann. of Math. (2) 165 (2007), 15–53.
  • A. Givental, Equivariant Gromov–Witten invariants, Internat. Math. Res. Notices 13 (1996), 613–663.
  • –––, A mirror theorem for toric complete intersections, Topological field theory, primitive forms and related topics (Kyoto, 1996), Progr. Math., 160, pp. 141–175, Birkhäuser, Boston, 1998.
  • –––, Symplectic geometry of Frobenius structures, Frobenius manifolds, Aspects Math., E36, pp. 91–112, Vieweg, Wiesbaden, 2004.
  • H. Iritani, Convergence of quantum cohomology by quantum Lefschetz, J. Reine Angew. Math. 610 (2007), 29–69.
  • –––, An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. Math. 222 (2009), 1016–1079.
  • Y.-P. Lee, H.-W. Lin, and C.-L. Wang, Invariance of quantum rings under ordinary flops, preprint, arXiv:1109.5540.
  • A. Popa, Two-point Gromov–Witten formulas for symplectic toric manifolds, preprint, arXiv:1206.2703.
  • A. Popa and A. Zinger, Mirror symmetry for closed, open, and unoriented Gromov–Witten invariants, preprint, arXiv:1010.1946.
  • H.-H. Tseng, Orbifold quantum Riemann–Roch, Lefschetz and Serre, Geom. Topol. 14 (2010), 1–81.
  • A. Zinger, Genus-zero two-point hyperplane integrals in the Gromov–Witten theory, Comm. Anal. Geom. 17 (2009), 955–999.
  • –––, The genus-0 Gromov–Witten invariants of projective complete intersections, preprint, arXiv:1106.1633.