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arXiv · 1706.09912

Computing a categorical Gromov-Witten invariant

Andrei Caldararu·Junwu Tu
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Abstract

We compute the $g=1, n=1$ B-model Gromov-Witten invariant of an elliptic curve E directly from the derived category D(E). More precisely, we carry out the computation of the categorical Gromov-Witten invariant defined by Costello using as target a cyclic $A_\infty$ model of D(E) described by Polishchuk. This is the first non-trivial computation of a positive genus categorical Gromov-Witten invariant, and the result agrees with the prediction of mirror symmetry: it matches the classical (non-categorical) Gromov-Witten invariants of a symplectic 2-torus computed by Dijkgraaf.

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Andrei Caldararu, Junwu Tu. 2017-07-11. Computing a categorical Gromov-Witten invariant. https://arxiv.org/abs/1706.09912

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