Spherical surfaces with conical points: systole inequality and moduli spaces with many connected components

Abstract

In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider some features of the forgetful map from the above moduli space of spherical surfaces with conical points to the associated moduli space of pointed Riemann surfaces, such as its properness, which follows from an explicit systole inequality that relates metric invariants (spherical systole) and conformal invariant (extremal systole).

arXiv comment63 pages, 22 figures. Final version

References in corpus (1)

• Fuchsian Equations with Three Non-Apparent Singularities

Cited by in corpus (9)

• Polyakov-Alvarez type comparison formulas for determinants of Laplacians on Riemann surfaces with conical singularities
• Conical metrics on Riemann surfaces, II: spherical metrics
• Moduli of spherical tori with one conical point
• Moduli spaces for Lamé functions and Abelian integrals of the second kind
• Spectral properties of reducible conical metrics
• Monodromy of Schwarzian equations with regular singularities
• Cone spherical metrics and stable vector bundles
• Irreducible cone spherical metrics and stable extensions of two line bundles
• Solution to SU(n+1) Toda system generated by spherical metrics