Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere

Pasquinelli, Irene

doi:10.1090/ecgd/299

Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere
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by Irene Pasquinelli PDF

Conform. Geom. Dyn. 20 (2016), 235-281 Request permission

Abstract:

Deligne and Mostow constructed a class of lattices in $PU(2,1)$ using monodromy of hypergeometric functions. Thurston reinterpreted them in terms of cone metrics on the sphere. In this spirit we construct a fundamental domain for the lattices with three fold symmetry in the list of Deligne and Mostow. This is a generalisation of the works of Boadi and Parker and gives a different interpretation of the fundamental domain constructed by Deraux, Falbel, and Paupert.

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