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

van Ittersum, J.-W.-M., Oberdieck, G., & Pixton, A. (2021). Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms. Selecta Mathematica, 27(4): 64. doi:10.1007/s00029-021-00673-y.

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Ittersum-Oberdieck-Pixton_Gromov-Witten theory of K3 surfaces and a Kaneko-Zagier equation for Jacobi forms_2021.pdf (Publisher version), 356KB
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https://doi.org/10.1007/s00029-021-00673-y (Publisher version)
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 Creators:
van Ittersum, Jan-Willem M.1, Author           
Oberdieck, Georg, Author
Pixton, Aaron, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Geometry, Number Theory
 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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 Dates: 2021
 Publication Status: Issued
 Pages: 30
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2007.03489
DOI: 10.1007/s00029-021-00673-y
 Degree: -

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Title: Selecta Mathematica
Source Genre: Journal
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Publ. Info: Birkhäuser
Pages: - Volume / Issue: 27 (4) Sequence Number: 64 Start / End Page: - Identifier: -