# Effective cones of blowups

September 26, 2022

The cone of effective divisors in a general algebraic variety is usually not polyhedral. It may have infinitely many extremal rays, and it may even be round. For toric varieties, however, the effective cone is always polyhedral. In this talk I will discuss the effective cone of a toric variety blown up at a point. More specifically, I consider blowups of weighted projective planes $P(a,b,c)$ and more general toric surfaces of Picard number 1. The problem here is to determine if the 2-dimensional effective cone of the blowup is closed or not. This problem relates to several classical problems about curves on algebraic surfaces. This is a joint work with Jose Gonzalez and Javier Gonzalez-Anaya.

**Time: **3:00-4:00pm

**Location: **MATH 126

**Seminar Website: **https://yifeng-huang-math.github.io/seminar_ubc_ag_22f.html