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arXiv · 1802.00424

Quantum cohomology and closed-string mirror symmetry for toric varieties

Jack Smith
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Abstract

We give a short new computation of the quantum cohomology of an arbitrary smooth toric variety $X$, by showing directly that the Kodaira-Spencer map of Fukaya-Oh-Ohta-Ono defines an isomorphism onto a suitable Jacobian ring. The proof is based on the purely algebraic fact that a class of generalised Jacobian rings associated to $X$ are free as modules over the Novikov ring. In contrast to previous results of this kind, $X$ need not be compact. When $X$ is monotone the presentation we obtain is completely explicit, using only well-known computations with the standard complex structure.

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Jack Smith. 2018-02-01. Quantum cohomology and closed-string mirror symmetry for toric varieties. https://arxiv.org/abs/1802.00424

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