Some Kähler structures on products of 2-spheres
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866909406609801216 |
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| author | Lafont, Jean-François Sorcar, Gangotryi Zheng, Fangyang |
| author_facet | Lafont, Jean-François Sorcar, Gangotryi Zheng, Fangyang |
| contents | We consider a family of Kähler structures on products of 2-spheres, arising from complex Bott manifolds. These are obtained via iterated $\mathbb P^1$-bundle constructions, generalizing the classical Hirzebruch surfaces. We show that the resulting Kähler structures all have identical Chern classes. We construct Bott diagrams, which are rooted forests with an edge labelling by positive integers, and show that these classify these Kähler structures up to biholomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1708_07984 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Some Kähler structures on products of 2-spheres Lafont, Jean-François Sorcar, Gangotryi Zheng, Fangyang Differential Geometry Algebraic Geometry Complex Variables 32Q15 (primary), 32L05, 32Q10, 53C55 (secondary) We consider a family of Kähler structures on products of 2-spheres, arising from complex Bott manifolds. These are obtained via iterated $\mathbb P^1$-bundle constructions, generalizing the classical Hirzebruch surfaces. We show that the resulting Kähler structures all have identical Chern classes. We construct Bott diagrams, which are rooted forests with an edge labelling by positive integers, and show that these classify these Kähler structures up to biholomorphism. |
| title | Some Kähler structures on products of 2-spheres |
| topic | Differential Geometry Algebraic Geometry Complex Variables 32Q15 (primary), 32L05, 32Q10, 53C55 (secondary) |
| url | https://arxiv.org/abs/1708.07984 |