Mori Dream Bonds and $\mathbb{C}^*$-actions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917919344033792 |
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| author | Barban, Lorenzo Romano, Eleonora A. Conde, Luis E. Solá Urbinati, Stefano |
| author_facet | Barban, Lorenzo Romano, Eleonora A. Conde, Luis E. Solá Urbinati, Stefano |
| contents | We construct a correspondence between Mori dream regions arising from small modifications of normal projective varieties and $\mathbb{C}^*$-actions on polarized pairs which are bordisms. Moreover, we show that the Mori dream regions constructed in this way admit a chamber decomposition on which the models are the geometric quotients of the $\mathbb{C}^*$-action. In addition we construct, from a given $\mathbb{C}^*$-action on a polarized pair for which there exist at least two admissible geometric quotients, a $\mathbb{C}^*$-equivariantly birational $\mathbb{C}^*$-variety, whose induced action is a bordism, called the pruning of the variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_09864 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mori Dream Bonds and $\mathbb{C}^*$-actions Barban, Lorenzo Romano, Eleonora A. Conde, Luis E. Solá Urbinati, Stefano Algebraic Geometry Primary 14L30, Secondary 14E30, 14L24, 14M17 We construct a correspondence between Mori dream regions arising from small modifications of normal projective varieties and $\mathbb{C}^*$-actions on polarized pairs which are bordisms. Moreover, we show that the Mori dream regions constructed in this way admit a chamber decomposition on which the models are the geometric quotients of the $\mathbb{C}^*$-action. In addition we construct, from a given $\mathbb{C}^*$-action on a polarized pair for which there exist at least two admissible geometric quotients, a $\mathbb{C}^*$-equivariantly birational $\mathbb{C}^*$-variety, whose induced action is a bordism, called the pruning of the variety. |
| title | Mori Dream Bonds and $\mathbb{C}^*$-actions |
| topic | Algebraic Geometry Primary 14L30, Secondary 14E30, 14L24, 14M17 |
| url | https://arxiv.org/abs/2207.09864 |