The aim of this paper is to study all the natural first steps of the minimal model program for the moduli space of stable pointed curves. We prove that they admit a modular interpretation, and we study their geometric properties. As a particular case, we recover the first few Hassett–Keel log canonical models. As a by-product, we produce many birational morphisms from the moduli space of stable pointed curves to alternative modular projective compactifications of the moduli space of pointed curves.

中文翻译：

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关于稳定点曲线模空间的最小模型程序的第一步

本文的目的是研究稳定尖曲线模空间的最小模型程序的所有自然第一步。我们证明它们承认模块化解释，并且我们研究它们的几何特性。作为一个特殊案例，我们恢复了前几个 Hassett–Keel 对数规范模型。作为副产品，我们从稳定尖曲线的模空间到尖曲线模空间的替代模射影紧化产生了许多双有理态射。