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Quantum cohomology of the Hilbert scheme of points in the plane

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We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points of ℂ2. The operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum Calogero-Sutherland many-body system. A relationship between the quantum cohomology of the Hilbert scheme and the Gromov-Witten/Donaldson-Thomas correspondence for local curves is proven.

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  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    A. Okounkov & R. Pandharipande

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  1. A. Okounkov
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  2. R. Pandharipande
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Correspondence to A. Okounkov.

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Okounkov, A., Pandharipande, R. Quantum cohomology of the Hilbert scheme of points in the plane. Invent. math. 179, 523–557 (2010). https://doi.org/10.1007/s00222-009-0223-5

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