Special Kähler structures, cubic differentials and hyperbolic metrics

• Andriy Haydys ^[1] ; Bin Xu ^[2]
  1. [1] University of Freiburg

     University of Freiburg

     Stadtkreis Freiburg im Breisgau, Alemania

     
  2. [2] University of Science and Technology of China

     University of Science and Technology of China

     China

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 3, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-00560-y
• Enlaces
  • Texto completo
• Resumen

  • We obtain necessary conditions for the existence of special Kähler structures with isolated singularities on compact Riemann surfaces. We prove that these conditions are also sufficient in the case of the Riemann sphere and, moreover, we determine the whole moduli space of special Kähler structures with fixed singularities. The tool we develop for this aim is a correspondence between special Kähler structures and pairs consisting of a cubic differential and a hyperbolic metric.