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The Quantum Orbifold Cohomology of Weighted Projective Spaces

Tom Coates·Alessio Corti·Yuan-Pin Lee·Hsian-Hua Tseng
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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. We also 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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Tom Coates, Alessio Corti, Yuan-Pin Lee, Hsian-Hua Tseng. 2006-08-20. The Quantum Orbifold Cohomology of Weighted Projective Spaces. https://arxiv.org/abs/math/0608481

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