Exceptional algebraic curves for infinite groups of $\textrm{PGL}(n,\mathbb{C})$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910924479135744 |
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| author | Cano, Angel Loeza, Luis Figueroa, Rodrigo Dávila |
| author_facet | Cano, Angel Loeza, Luis Figueroa, Rodrigo Dávila |
| contents | We classify algebraic curves in $\mathbb{CP}^{n}$ ($n \geq 2$) that are invariant under an infinite subgroup of $\operatorname{PGL}(n+1,\mathbb{C})$. In particular, we prove that any irreducible, non-degenerate, one-dimensional algebraic set in $\mathbb{CP}^{n}$ invariant under an infinite subgroup of $\operatorname{Aut}(\mathbb{CP}^{n})$ must be projectively equivalent to a monomial curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02620 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exceptional algebraic curves for infinite groups of $\textrm{PGL}(n,\mathbb{C})$ Cano, Angel Loeza, Luis Figueroa, Rodrigo Dávila Algebraic Geometry Dynamical Systems We classify algebraic curves in $\mathbb{CP}^{n}$ ($n \geq 2$) that are invariant under an infinite subgroup of $\operatorname{PGL}(n+1,\mathbb{C})$. In particular, we prove that any irreducible, non-degenerate, one-dimensional algebraic set in $\mathbb{CP}^{n}$ invariant under an infinite subgroup of $\operatorname{Aut}(\mathbb{CP}^{n})$ must be projectively equivalent to a monomial curve. |
| title | Exceptional algebraic curves for infinite groups of $\textrm{PGL}(n,\mathbb{C})$ |
| topic | Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2303.02620 |