On terminal Fano 3-folds with 2-torus action
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2014
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| Acceso en línea: | |
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| _version_ | 1866909676062375936 |
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| author | Bechtold, Benjamin Huggenberger, Elaine Hausen, Juergen Nicolussi, Michele |
| author_facet | Bechtold, Benjamin Huggenberger, Elaine Hausen, Juergen Nicolussi, Michele |
| contents | We classify the terminal Fano threefolds of Picard number one that come with an effective action of a two-torus. Our approach applies also to higher dimensions and generalizes the correspondence between toric Fano varieties and lattice polytopes: to any Fano variety with a complete intersection Cox ring we associate its "anti canonical complex", which is a certain polyhedral complex living in the lattice of one parameter groups of an ambient toric variety. For resolutions constructed via the tropical variety, the lattice points inside the anticanonical complex control the discrepancies. This leads, for example, to simple characterizations of terminality and canonicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1412_8153 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | On terminal Fano 3-folds with 2-torus action Bechtold, Benjamin Huggenberger, Elaine Hausen, Juergen Nicolussi, Michele Algebraic Geometry 14J45, 14J30, 14L30 We classify the terminal Fano threefolds of Picard number one that come with an effective action of a two-torus. Our approach applies also to higher dimensions and generalizes the correspondence between toric Fano varieties and lattice polytopes: to any Fano variety with a complete intersection Cox ring we associate its "anti canonical complex", which is a certain polyhedral complex living in the lattice of one parameter groups of an ambient toric variety. For resolutions constructed via the tropical variety, the lattice points inside the anticanonical complex control the discrepancies. This leads, for example, to simple characterizations of terminality and canonicity. |
| title | On terminal Fano 3-folds with 2-torus action |
| topic | Algebraic Geometry 14J45, 14J30, 14L30 |
| url | https://arxiv.org/abs/1412.8153 |