Cones of divisors on $\mathbb{P}^3$ blown up at eight very general points

Abstract

Let $X$ be the blowup of $\mathbb{P}^3$ at eight very general points. We give a complete description of its nef and effective cones. Moreover, we show that there exists a rational polyhedral fundamental domain for the action of a certain Weyl group on the effective movable cone of $X$.