The Quantum Orbifold Cohomology of Weighted Projective Spaces
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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Cite
@article{arxiv.math/0608481,
title = {The Quantum Orbifold Cohomology of Weighted Projective Spaces},
author = {Tom Coates and Alessio Corti and Yuan-Pin Lee and Hsian-Hua Tseng},
journal= {arXiv preprint arXiv:math/0608481},
year = {2022}
}
Comments
LaTeX, 45 pages. Version 2: minor changes. Version 3: further typos corrected. Version 4: minor changes. Version 5: major changes to the exposition (especially in Section 3), title changed. Version 6: this is the final version; to appear in Acta Mathematica