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<p>Our goal is twofold. On one hand, we show that the cones of divisors ample in codimension <i>k</i> on a Mori dream space are rational polyhedral. On the other hand, we study the duality between such cones and the cones of <i>k</i>-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.</p>

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Duality and polyhedrality of cones for Mori dream spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月27日

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

摘要

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.