Toric manifolds over 3-polytopes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| _version_ | 1866908820766195712 |
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| author | Ayzenberg, Anton |
| author_facet | Ayzenberg, Anton |
| contents | In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes, that do not correspond to any smooth projective toric variety. We restate the proof of the second claim which does not refer to complicated algebro-geometrical technique. If follows from these results that any fullerene supports quasitoric manifolds but does not support smooth projective toric varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1607_03377 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Toric manifolds over 3-polytopes Ayzenberg, Anton Algebraic Topology Algebraic Geometry Combinatorics Primary 52B10, 14M25, 57N16, Secondary 05E40, 05E45, 52B20, 14C25, 53D05, 57N65, 57R19 In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes, that do not correspond to any smooth projective toric variety. We restate the proof of the second claim which does not refer to complicated algebro-geometrical technique. If follows from these results that any fullerene supports quasitoric manifolds but does not support smooth projective toric varieties. |
| title | Toric manifolds over 3-polytopes |
| topic | Algebraic Topology Algebraic Geometry Combinatorics Primary 52B10, 14M25, 57N16, Secondary 05E40, 05E45, 52B20, 14C25, 53D05, 57N65, 57R19 |
| url | https://arxiv.org/abs/1607.03377 |