Collections of parabolic orbits in homogeneous spaces, homogeneous dynamics and hyperkahler geometry
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2016
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| _version_ | 1866916316634415104 |
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| author | Amerik, Ekaterina Verbitsky, Misha |
| author_facet | Amerik, Ekaterina Verbitsky, Misha |
| contents | Let $M$ be a hyperkähler manifold with $b_2(M)\geq 5$. We improve our earlier results on the Morrison-Kawamata cone conjecture by showing that the Beauville-Bogomolov square of the primitive MBM classes (i.e. the classes whose orthogonal hyperplanes bound the Kähler cone in the positive cone, or, in other words, the classes of negative extremal rational curves on deformations of $M$) is bounded in absolute value by a number depending only on the deformation class of $M$. The proof uses ergodic theory on homogeneous spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1604_03927 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Collections of parabolic orbits in homogeneous spaces, homogeneous dynamics and hyperkahler geometry Amerik, Ekaterina Verbitsky, Misha Algebraic Geometry Differential Geometry 14E30, 53C26 Let $M$ be a hyperkähler manifold with $b_2(M)\geq 5$. We improve our earlier results on the Morrison-Kawamata cone conjecture by showing that the Beauville-Bogomolov square of the primitive MBM classes (i.e. the classes whose orthogonal hyperplanes bound the Kähler cone in the positive cone, or, in other words, the classes of negative extremal rational curves on deformations of $M$) is bounded in absolute value by a number depending only on the deformation class of $M$. The proof uses ergodic theory on homogeneous spaces. |
| title | Collections of parabolic orbits in homogeneous spaces, homogeneous dynamics and hyperkahler geometry |
| topic | Algebraic Geometry Differential Geometry 14E30, 53C26 |
| url | https://arxiv.org/abs/1604.03927 |