School of Mathematics Seminars and Lectures

Blown-up toric surfaces with non-polyhedral effective cone

by Prof. Ana-Maria Castravet (Universite de Versailles)

Friday, December 18, 2020 from to (Asia/Kolkata)
at Via Zoom
Description
Abstract:I will report on recent joint work with Antonio Laface, Jenia Tevelev and Luca Ugaglia. We construct examples of projective toric surfaces whose blow-up at a general point has a non-polyhedral pseudoeffective cone, both in characteristic 0 and in prime characteristic. As a consequence, we prove that the pseudo-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. In particular, these moduli spaces are not Mori dream spaces even in positive characteristic.