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QUANTUM COHOMOLOGY AND CLOSED-STRING MIRROR SYMMETRY FOR TORIC VARIETIES
Quarterly Journal of Mathematics ( IF 0.636 ) Pub Date : 2020-01-11 , DOI: 10.1093/qmathj/haz056
Smith J.

We give a short new computation of the quantum cohomology of an arbitrary smooth (semiprojective) toric variety $X$, by showing directly that the Kodaira–Spencer map of Fukaya–Oh–Ohta–Ono defines an isomorphism onto a suitable Jacobian ring. In contrast to previous results of this kind, $X$ need not be compact. The proof is based on the purely algebraic fact that a class of generalized Jacobian rings associated to $X$ are free as modules over the Novikov ring. When $X$ is monotone the presentation we obtain is completely explicit, using only well-known computations with the standard complex structure.
更新日期:2020-01-13

 

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