Blown-up toric surfaces with non-polyhedral effective cone

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 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. In particular, these moduli spaces are not Mori dream spaces even in positive characteristic.

algebraic geometry

Audience: researchers in the topic

EDGE 2020 (online)

Series comments: The workshop subject will be EXPLICIT K-STABILITY AND MODULI PROBLEMS. Webpage to follow. Please, do register using the form to get a link to connect. On Monday and Thursday we will have a social (bring your own drink).