Equivariant automorphism group and real forms of complexity-one varieties
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911426531033088 |
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| author | Arteche, Giancarlo Lucchini Terpereau, Ronan |
| author_facet | Arteche, Giancarlo Lucchini Terpereau, Ronan |
| contents | Let G be a connected reductive algebraic group over a perfect field. We study the representability of the equivariant automorphism group of G-varieties. For a broad class of complexity-one G-varieties, we show that this group is representable by a group scheme locally of finite type when the base field has characteristic zero. We also establish representability by a linear algebraic group in the case of almost homogeneous G-varieties of arbitrary complexity. Finally, using an exact sequence description of the equivariant automorphism group, we deduce that complexity-one G-varieties with representable equivariant automorphism group admit only finitely many real forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant automorphism group and real forms of complexity-one varieties Arteche, Giancarlo Lucchini Terpereau, Ronan Algebraic Geometry Primary 14L30, 14J50, 14M17, 14P99, Secondary 14L15, 14D06, 14F06, 14G27 Let G be a connected reductive algebraic group over a perfect field. We study the representability of the equivariant automorphism group of G-varieties. For a broad class of complexity-one G-varieties, we show that this group is representable by a group scheme locally of finite type when the base field has characteristic zero. We also establish representability by a linear algebraic group in the case of almost homogeneous G-varieties of arbitrary complexity. Finally, using an exact sequence description of the equivariant automorphism group, we deduce that complexity-one G-varieties with representable equivariant automorphism group admit only finitely many real forms. |
| title | Equivariant automorphism group and real forms of complexity-one varieties |
| topic | Algebraic Geometry Primary 14L30, 14J50, 14M17, 14P99, Secondary 14L15, 14D06, 14F06, 14G27 |
| url | https://arxiv.org/abs/2507.18475 |