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arXiv · 2007.03489

Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms

Jan-Willem van Ittersum·Georg Oberdieck·Aaron Pixton
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Abstract

We prove the existence of quasi-Jacobi form solutions for an analogue of the Kaneko--Zagier differential equation for Jacobi forms. The transformation properties of the solutions under the Jacobi group are derived. A special feature of the solutions is the polynomial dependence of the index parameter. The results yield an explicit conjectural description for all double ramification cycle integrals in the Gromov--Witten theory of K3 surfaces.

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Jan-Willem van Ittersum, Georg Oberdieck, Aaron Pixton. 2020-07-07. Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms. https://arxiv.org/abs/2007.03489

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