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Toric arc schemes and quantum cohomology of toric varieties

Sergey Arkhipov·Mikhail Kapranov
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Abstract

We describe the quantum cohomology ring of a toric Fano variety $X$ in terms of the usual topological cohomology ring for an auxiliary infinite-dimensional scheme. This scheme is a part of an algebro-geometric model for the universal cover of the space of free loops with values in $X$.

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Sergey Arkhipov, Mikhail Kapranov. 2005-01-18. Toric arc schemes and quantum cohomology of toric varieties. https://arxiv.org/abs/math/0410054

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