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Abstract des Vortrages von Ana-Maria Castravet

Birational geometry of moduli spaces of stable rational curves

I will report on joint work with Tevelev on the birational geometry of the Grothendieck-Knudsen moduli space of stable rational curves with n markings. We prove that for n > 133 this space is not a Mori Dream Space, thus answering a question of Hu and Keel.