Chow quotients of ${\mathbb C}^*$-actions on convex varieties
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908838362349568 |
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| author | Occhetta, Gianluca Conde, Luis E. Solá |
| author_facet | Occhetta, Gianluca Conde, Luis E. Solá |
| contents | In this paper we study the Chow quotient ${\mathcal C}X$ of a convex variety $X$ of Picard number one by the action of a one dimensional torus having no non-trivial finite isotropy. Examples of these actions can be found in the rational homogeneous framework. We prove that the subvariety of ${\mathcal C}X$ parametrizing reducible torus-invariant cycles is a simple normal crossing divisor, we compute the Nef and Mori cones of ${\mathcal C}X$, and its anticanonical divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chow quotients of ${\mathbb C}^*$-actions on convex varieties Occhetta, Gianluca Conde, Luis E. Solá Algebraic Geometry Primary 14L30, Secondary 14E30, 14L24, 14M17, 14J45 In this paper we study the Chow quotient ${\mathcal C}X$ of a convex variety $X$ of Picard number one by the action of a one dimensional torus having no non-trivial finite isotropy. Examples of these actions can be found in the rational homogeneous framework. We prove that the subvariety of ${\mathcal C}X$ parametrizing reducible torus-invariant cycles is a simple normal crossing divisor, we compute the Nef and Mori cones of ${\mathcal C}X$, and its anticanonical divisor. |
| title | Chow quotients of ${\mathbb C}^*$-actions on convex varieties |
| topic | Algebraic Geometry Primary 14L30, Secondary 14E30, 14L24, 14M17, 14J45 |
| url | https://arxiv.org/abs/2503.19663 |