Constructibility aspects of the cone conjecture
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911635050856448 |
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| author | Serebrennikov, Daniil |
| author_facet | Serebrennikov, Daniil |
| contents | We establish two consequences of the Kawamata--Morrison--Totaro cone conjecture, and prove them unconditionally in all dimensions. First, for a K-trivial variety, the natural action of its automorphism group on the set of ample divisor classes of fixed volume has only finitely many orbits. Second, the number of (isomorphism classes of) minimal models for a given K-trivial variety is finite if these models admit a bounded polarization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27303 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constructibility aspects of the cone conjecture Serebrennikov, Daniil Algebraic Geometry We establish two consequences of the Kawamata--Morrison--Totaro cone conjecture, and prove them unconditionally in all dimensions. First, for a K-trivial variety, the natural action of its automorphism group on the set of ample divisor classes of fixed volume has only finitely many orbits. Second, the number of (isomorphism classes of) minimal models for a given K-trivial variety is finite if these models admit a bounded polarization. |
| title | Constructibility aspects of the cone conjecture |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.27303 |