Eric Jovinelly : Extreme Divisors on M_{0,7} and Differences over Characteristic 2

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

April 25, 2022, 3 p.m.

In

Zoom

Abstract

The cone of effective divisors controls the rational maps from a variety. We study this important object for M_{0,n}, the moduli space of stable rational curves with n markings. Fulton once conjectured the effective cones for each n would follow a certain combinatorial pattern. However, this pattern holds true only for n < 6. Despite many subsequent attempts to describe the effective cones for all n, we still lack even a conjectural description. We study the simplest open case, n=7, and identify the first known difference between characteristic 0 and characteristic p. Although a full description of the effective cone for n=7 remains open, our methods allowed us to compute the entire effective cones of spaces associated with other stability conditions.