Dihedral monodromy of cone spherical metrics

Quentin Gendron; Guillaume Tahar

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arXiv · 2112.00594

Dihedral monodromy of cone spherical metrics

Quentin Gendron·Guillaume Tahar

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Abstract

Among metrics of constant positive curvature on a punctured compact Riemann surface with conical singularities at the punctures, dihedral monodromy means that the action of the monodromy group globally preserves a pair of antipodal points. Using recent results about local invariants of quadratic differentials, we give a complete characterization of the set of conical angles realized by some cone spherical metric with dihedral monodromy.

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Quentin Gendron, Guillaume Tahar. 2021-12-01. Dihedral monodromy of cone spherical metrics. https://arxiv.org/abs/2112.00594

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