The quantum orbifold cohomology of weighted projective spaces |
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Authors: | Tom Coates Alessio Corti Yuan-Pin Lee Hsian-Hua Tseng |
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Institution: | 1.Department of Mathematics,Imperial College London,London,U.K.;2.Department of Mathematics,University of Utah,Salt Lake City,U.S.A.;3.Department of Mathematics,University of British Columbia,Vancouver,Canada |
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Abstract: | 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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