Session S35 - Moduli Spaces in Algebraic Geometry and Applications

Wednesday, July 14, 12:00 ~ 12:40 UTC-3

Blown-up toric surfaces with non-polyhedral effective cone

Ana-Maria Castravet

Université de Versailles, France   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We construct examples of projective toric surfaces whose blow-up at a general point has a non-polyhedral effective cone, both in characteristic 0 and in prime characteristic. As a consequence, we prove that the effective cone of the Grothendieck-Knudsen moduli space of stable, n-pointed, rational stable curves, is not polyhedral if n>=10 in characteristic 0 and in positive characteristic for an infinite set of primes of positive density.

Joint work with Antonio Laface (Universidad de Concepcion, Chile), Jenia Tevelev (University of Massachusetts at Amherst, USA) and Luca Ugaglia (Universita degli studi di Palermo, Italy).

View abstract PDF