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arXiv · 2305.18536

Duality and polyhedrality of cones for Mori dream spaces

Maria Chiara Brambilla·Olivia Dumitrescu·Elisa Postinghel·Luis José Santana Sánchez
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Abstract

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.

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Maria Chiara Brambilla, Olivia Dumitrescu, Elisa Postinghel, Luis José Santana Sánchez. 2025-02-21. Duality and polyhedrality of cones for Mori dream spaces. https://doi.org/10.1007/s00209-025-03699-6

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