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).

中文翻译：

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具有圆锥形点的球面：收缩不等式和具有许多连接组件的模空间

在本文中，我们讨论具有指定角度的圆锥奇点（例如其非空性和连通性）的连通，紧凑，可定向表面上的球形度量的模空间的许多特征。我们还考虑了上述健忘映射的一些特征，这些特征从具有圆锥点的球面的上述模空间到尖锐黎曼曲面的相关模空间，例如其正确性（源自与度量不变量（球收缩）相关的显式收缩不等式）和保形不变（收缩期末期）。