Duality and polyhedrality of cones for Mori dream spaces
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.
Authors
- Elisa Postinghel (ORCID: https://orcid.org/0000-0003-0874-6045)
- Maria Chiara Brambilla (ORCID: https://orcid.org/0000-0002-8637-4438)
- Luis José Santana Sánchez (ORCID: https://orcid.org/0000-0002-9197-1376)
- Olivia Dumitrescu (ORCID: https://orcid.org/0000-0001-6396-522X)
Institutions
- University of North Carolina at Chapel Hill (US)
- Marche Polytechnic University (IT)
- Universidad de La Laguna (ES)
- University of Trento (IT)
- Max Planck Institute for Mathematics (DE)
Publication Details
- Journal
- Mathematische Zeitschrift
- Published
- 2025-02-27
- DOI
- https://doi.org/10.1007/s00209-025-03699-6
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Università degli Studi di Trento
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni