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Moduli Spaces of Marked Branched Projective Structures on Surfaces by Billon, Gustave is a scholarly article available to read on EtoBox.

What is Moduli Spaces of Marked Branched Projective Structures on Surfaces about?

We show that the moduli space of marked branched projective structures of genus g and branching degree n is a complex analytic space. In the case g > 1 we show that this moduli space is of dimension 6 g - 6 + n and we characterize its singular points in terms of their monodromy. We introduce a notion of branching class, that is an infinitesimal description of branched projective structures at the branched points. We show that the space of marked branching classes of genus g and branching degree n is a complex manifold. We show that if n < 2g-2 the space of branched projective structures is an affine bundle over the space of branching classes, while if n > 4g-4 the former is an analytic subspace of the latter.

Author

Billon, Gustave

Published

2022

Language

EN