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

On the first steps of the minimal model program for the moduli space of stable pointed curves