Toric Sasaki–Einstein metrics with conical singularities

• Martin de Borbon ^[1] ; Eveline Legendre ^[2]
  1. [1] King's College London

     King's College London

     Reino Unido

     
  2. [2] Université de Toulouse

     Université de Toulouse

     Arrondissement de Toulouse, Francia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 3, 2022, 45 págs.
• Idioma: inglés
• Enlaces
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• Resumen

  • We show that any toric Kähler cone with smooth compact cross-section admits a family of Calabi–Yau cone metrics with conical singularities along its toric divisors.

    The family is parametrized by the Reeb cone and the angles are given explicitly in terms of the Reeb vector field. The result is optimal, in the sense that any toric Calabi–Yau cone metric with conical singularities along the toric divisor (and smooth elsewhere) belongs to this family. We also provide examples and interpret our results in terms of Sasaki–Einstein metrics.