Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms
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...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
02 July 2021
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| In: |
Selecta mathematica
Year: 2021, Volume: 27, Issue: 4, Pages: 1-30 |
| ISSN: | 1420-9020 |
| DOI: | 10.1007/s00029-021-00673-y |
| Online Access: | Resolving-System, kostenfrei, Volltext: https://doi.org/10.1007/s00029-021-00673-y Verlag, kostenfrei, Volltext: https://link.springer.com/article/10.1007/s00029-021-00673-y 
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| Author Notes: | Jan-Willem van Ittersum, Georg Oberdieck, Aaron Pixton |
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| 520 | |a 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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