Polyhedral Fubini-Study metrics with cone singularities along the braid arrangement
Martin de Borbon (King’s College London)
Classical work of Klein on Gauss' hypergeometric equation leads to a classification of metrics with constant curvature on the 2-sphere and cone singularities at three distinct points (as pointed out in modern terms by Alexandre Eremenko in 2003). The work of Klein is extended to higher dimensions by Deligne-Mostow, who analyse the monodromy representation of Lauricella's hypergeometric system. In joint work with Dmitri Panov we show that when the monodromy is unitary then the metric completion is polyhedral, leading to new interesting examples of polyhedral Kahler metrics.
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