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

• Jan-Willem van Ittersum ^[2] ; Georg Oberdieck ^[3] ; Aaron Pixton ^[1]
  1. [1] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     
  2. [2] Universiteit Utrecht, Paises Bajos; Max-Planck-Institut für Mathematik, Alemania
  3. [3] Universität Bonn, Alemania

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 4, 2021
• Idioma: inglés
• DOI: 10.1007/s00029-021-00673-y
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• Resumen

  • 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.