The quantum orbifold cohomology of weighted projective spaces

Tom Coates Department of Mathematics, Imperial College London Alessio Corti Department of Mathematics, Imperial College London Yuan-Pin Lee Department of Mathematics, University of Utah Hsian-Hua Tseng Department of Mathematics, University of British Columbia

TBD mathscidoc:1701.332002

Acta Mathematica, 202, (2), 139-193, 2006.10
We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental’s heuristic argument, which relates small quantum cohomology to$S$^{1}-equivariant Floer cohomology of loop space, to weighted projective spaces and use this to conjecture an explicit formula for the small$J$-function, a generating function for certain genus-zero Gromov–Witten invariants. We prove this conjecture using a method due to Bertram. This provides the first non-trivial example of a family of orbifolds of arbitrary dimension for which the small quantum orbifold cohomology is known. In addition we obtain formulas for the small$J$-functions of weighted projective complete intersections satisfying a combinatorial condition; this condition naturally singles out the class of orbifolds with terminal singularities.
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@inproceedings{tom2006the,
  title={The quantum orbifold cohomology of weighted projective spaces},
  author={Tom Coates, Alessio Corti, Yuan-Pin Lee, and Hsian-Hua Tseng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203352992698711},
  booktitle={Acta Mathematica},
  volume={202},
  number={2},
  pages={139-193},
  year={2006},
}
Tom Coates, Alessio Corti, Yuan-Pin Lee, and Hsian-Hua Tseng. The quantum orbifold cohomology of weighted projective spaces. 2006. Vol. 202. In Acta Mathematica. pp.139-193. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203352992698711.
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