Smooth projective varieties with a torus action of complexity 1 and Picard number 2
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arXiv
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| Format: | Preprint |
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2016
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| _version_ | 1866911039830884352 |
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| author | Fahrner, Anne Hausen, Juergen Nicolussi, Michele |
| author_facet | Fahrner, Anne Hausen, Juergen Nicolussi, Michele |
| contents | We give an explicit description of all smooth varieties with a torus action of complexity one having Picard number at most two. As a consequence, we classify in every dimension the smooth (almost) Fano varieties with a torus action of complexity one having Picard number two. It turns out that all the Fano examples are obtained via an iterated generalized cone construction from a series of smooth varieties of dimension at most seven. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1602_04360 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Smooth projective varieties with a torus action of complexity 1 and Picard number 2 Fahrner, Anne Hausen, Juergen Nicolussi, Michele Algebraic Geometry 14J45, 14L30 We give an explicit description of all smooth varieties with a torus action of complexity one having Picard number at most two. As a consequence, we classify in every dimension the smooth (almost) Fano varieties with a torus action of complexity one having Picard number two. It turns out that all the Fano examples are obtained via an iterated generalized cone construction from a series of smooth varieties of dimension at most seven. |
| title | Smooth projective varieties with a torus action of complexity 1 and Picard number 2 |
| topic | Algebraic Geometry 14J45, 14L30 |
| url | https://arxiv.org/abs/1602.04360 |