Small bandwidth ${\mathbb C}^*$-actions and birational geometry
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
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| _version_ | 1866910737982554112 |
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| author | Occhetta, Gianluca Romano, Eleonora A. Conde, Luis E. Solá Wiśniewski, Jarosław A. |
| author_facet | Occhetta, Gianluca Romano, Eleonora A. Conde, Luis E. Solá Wiśniewski, Jarosław A. |
| contents | In this paper we study smooth projective varieties and polarized pairs with an action of a one dimensional complex torus. As a main tool, we define birational geometric counterparts of these actions, that, under certain assumptions, encode the information necessary to reconstruct them. In particular, we consider some cases of actions of low complexity -- measured in terms of two invariants of the action, called bandwidth and bordism rank -- and discuss how they are determined by well known birational transformations, namely Atiyah flips and Cremona transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_12129 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Small bandwidth ${\mathbb C}^*$-actions and birational geometry Occhetta, Gianluca Romano, Eleonora A. Conde, Luis E. Solá Wiśniewski, Jarosław A. Algebraic Geometry In this paper we study smooth projective varieties and polarized pairs with an action of a one dimensional complex torus. As a main tool, we define birational geometric counterparts of these actions, that, under certain assumptions, encode the information necessary to reconstruct them. In particular, we consider some cases of actions of low complexity -- measured in terms of two invariants of the action, called bandwidth and bordism rank -- and discuss how they are determined by well known birational transformations, namely Atiyah flips and Cremona transformations. |
| title | Small bandwidth ${\mathbb C}^*$-actions and birational geometry |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1911.12129 |