Surjective rational maps and del Pezzo surfaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916770666774528 |
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| author | Karzhemanov, Ilya Lekontseva, Anna |
| author_facet | Karzhemanov, Ilya Lekontseva, Anna |
| contents | We study surjective (not necessarily regular) rational endomorphisms $f$ of smooth del Pezzo surfaces $X$. We prove that under certain natural non\,-\,degeneracy condition $f$ can have degree bigger than $1$ only when $(-K_X^2) > 5$. Some structural properties of $f$ in the case $X = \p^2$ are also established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01835 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Surjective rational maps and del Pezzo surfaces Karzhemanov, Ilya Lekontseva, Anna Algebraic Geometry We study surjective (not necessarily regular) rational endomorphisms $f$ of smooth del Pezzo surfaces $X$. We prove that under certain natural non\,-\,degeneracy condition $f$ can have degree bigger than $1$ only when $(-K_X^2) > 5$. Some structural properties of $f$ in the case $X = \p^2$ are also established. |
| title | Surjective rational maps and del Pezzo surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2311.01835 |