Characterizing Varieties Using Birational Transformations
Fuente:
arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917119275302912 |
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| author | Chen, Nathan Esser, Louis Regeta, Andriy Urech, Christian van Santen, Immanuel |
| author_facet | Chen, Nathan Esser, Louis Regeta, Andriy Urech, Christian van Santen, Immanuel |
| contents | Suppose $X$ is an irreducible complex variety. We show that when $X$ is ruled, the group of birational transformations $Bir(X)$, as a group, determines $X$ up to birational transformations and automorphisms of the base field. In contrast, we demonstrate that this same property never holds for non-uniruled varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing Varieties Using Birational Transformations Chen, Nathan Esser, Louis Regeta, Andriy Urech, Christian van Santen, Immanuel Algebraic Geometry 4E07, 14L30 Suppose $X$ is an irreducible complex variety. We show that when $X$ is ruled, the group of birational transformations $Bir(X)$, as a group, determines $X$ up to birational transformations and automorphisms of the base field. In contrast, we demonstrate that this same property never holds for non-uniruled varieties. |
| title | Characterizing Varieties Using Birational Transformations |
| topic | Algebraic Geometry 4E07, 14L30 |
| url | https://arxiv.org/abs/2512.02837 |