Birational Geometry of Moduli Spaces of Curves - Lecture 3
Centre International de Rencontres Mathématiques via YouTube
Overview
Explore a 56-minute mathematics lecture from the Centre International de Rencontres Mathématiques that delves into the Grothendieck-Knudsen moduli space of stable rational curves with n markings. Learn about this fundamental moduli space's properties as a smooth projective variety, its explicit description as a blow-up of projective space, and its strata corresponding to nodal curves. Discover the current understanding of its Mori cone of curves, known only for n up to 7, and examine why the cones of effective divisors are not finitely generated when n is at least 10 in all characteristics. Investigate elliptic pairs and Lang-Trotter polygons, understanding how the finite generation of effective cones of blow-ups of certain toric surfaces relates to elliptic curve arithmetic. Recorded during the "Algebraic Geometry and Complex Geometry" thematic meeting in Marseille, France, this lecture features collaborative research with Antonio Laface, Jenia Tevelev, and Luca Ugaglia, available with chapter markers, keywords, abstracts, and comprehensive mathematical classifications through CIRM's Audiovisual Mathematics Library.
Syllabus
Ana-Maria Castravet : Birational geometry of moduli spaces of curves - Lecture 3
Taught by
Centre International de Rencontres Mathématiques