Birational Geometry of Moduli Spaces of Curves - Lecture 2

Explore a 54-minute mathematics lecture focusing on the Grothendieck-Knudsen moduli space of stable rational curves and their markings, delivered at the Centre International de Rencontres Mathématiques. Delve into the properties of this fundamental moduli space, examining its structure as a smooth projective variety and its relationship to blow-ups of projective space. Learn about the strata corresponding to nodal curves, their similarities to torus invariant strata of toric varieties, and investigate the Mori cone of curves conjecture. Examine the non-finite generation of cones of effective divisors in all characteristics when n≥10. Discover the concepts of elliptic pairs and Lang-Trotter polygons, understanding their connection between effective cones of blow-ups of toric surfaces and elliptic curve arithmetic. Access this recorded lecture from the "Algebraic Geometry and Complex Geometry" thematic meeting, complete with chapter markers, keywords, abstracts, and comprehensive mathematical classifications through CIRM's Audiovisual Mathematics Library.