Birational Geometry of Moduli Spaces of Curves - Lecture 1

Explore a detailed mathematics lecture examining the Grothendieck-Knudsen moduli space of stable rational curves with n markings, focusing on its properties as a smooth projective variety and its relationship to blow-ups of projective space. Delve into the complexities of Mori cone curves, their strata generation properties for n values up to 7, and investigate why effective divisor cones become infinitely generated in all characteristics when n reaches 10 or higher. Learn about elliptic pairs and Lang-Trotter polygons, understanding their connection between effective cone generation in toric surface blow-ups and elliptic curve arithmetic. Recorded during the "Algebraic Geometry and Complex Geometry" thematic meeting at the Centre International de Rencontres Mathématiques in Marseille, this 49-minute lecture features interactive elements including chapter markers, keywords, abstracts, and comprehensive mathematical classifications accessible through CIRM's Audiovisual Mathematics Library.