Rational homogeneous spaces as geometric realizations of birational transformations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916666775961600 |
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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 | A geometric realization of a birational map $ψ$ among two complex projective varieties is a variety $X$ endowed with a $\mathbb{C}^*$-action inducing $ψ$ as the natural birational map among two extremal geometric quotients. In this paper we study geometric realizations of some classic birational maps --inversion maps, special Cremona transformations, special birational transformations of type $(2,1)$--, by considering $\mathbb{C}^*$-actions on certain rational homogeneous spaces and their subvarieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_15130 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Rational homogeneous spaces as geometric realizations of birational transformations Occhetta, Gianluca Romano, Eleonora A. Conde, Luis E. Solá Wiśniewski, Jarosław A. Algebraic Geometry Primary 14L30, Secondary 14E30, 14L24, 14M17 A geometric realization of a birational map $ψ$ among two complex projective varieties is a variety $X$ endowed with a $\mathbb{C}^*$-action inducing $ψ$ as the natural birational map among two extremal geometric quotients. In this paper we study geometric realizations of some classic birational maps --inversion maps, special Cremona transformations, special birational transformations of type $(2,1)$--, by considering $\mathbb{C}^*$-actions on certain rational homogeneous spaces and their subvarieties. |
| title | Rational homogeneous spaces as geometric realizations of birational transformations |
| topic | Algebraic Geometry Primary 14L30, Secondary 14E30, 14L24, 14M17 |
| url | https://arxiv.org/abs/2112.15130 |