Duality and polyhedrality of cones for Mori dream spaces

Maria Chiara Brambilla, Olivia Dumitrescu, Elisa Postinghel, Luis José Santana Sánchez

Published 2023-05-29Version 1

Our goal is twofold. On one hand we show that the cones of divisors ample in codimension $k$ on a Mori dream space are rational polyhedral. On the other hand we study the duality between such cones and the cones of $k$-moving curves by means of the Mori chamber decomposition of the former. We give a new proof of the weak duality property (already proved by Payne and Choi) and we exhibit an interesting family of examples for which strong duality holds.