Let $S$ be an orientable, finite-type surface with negative Euler characteristic. The augmented moduli space of convex real projective structures on $S$ was first defined and topologized by the first author. In this paper, we give an explicit description of this topology using explicit coordinates. More precisely, given every point in this augmented moduli space, we find explicit continuous coordinates on the quotient of a suitable open neighborhood about this point by a suitable subgroup of the mapping class group of $S$. Using this, we give a simpler proof of the fact that the augmented moduli space of convex real projective structures on $S$ is homeomorphic to the orbifold vector bundle of regular cubic differentials over the Deligne–Mumford compactification of the moduli space of Riemann surfaces homeomorphic to $S$.

中文翻译：

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凸 RP2 结构增广模空间上的坐标

让 $秒$是具有负欧拉特性的可定向有限型曲面。凸实射影结构的增广模空间$秒$由第一作者首先定义和拓扑。在本文中，我们使用显式坐标对该拓扑进行了显式描述。更准确地说，给定这个增广模空间中的每个点，我们通过映射类群的一个合适的子群找到关于这个点的合适的开邻域的商的显式连续坐标$秒$. 使用这个，我们给出了一个更简单的证明，即凸实射影结构的增广模空间在$秒$ 同胚于黎曼曲面模空间的 Deligne-Mumford 紧化上规则三次微分的轨道向量丛同胚 $秒$.