Smooth minimal surfaces of general type with $p_g=0, K^2=7$ and involutions
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908430099283968 |
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| author | Chen, Yifan Shin, YongJoo Zhang, Han |
| author_facet | Chen, Yifan Shin, YongJoo Zhang, Han |
| contents | Lee and the second named author studied involutions on smooth minimal surfaces $S$ of general type with $p_g(S)=0$ and $K_S^2=7$. They gave the possibilities of the birational models $W$ of the quotients and the branch divisors $B_0$ induced by involutions $σ$ on the surfaces $S$.
In this paper we improve and refine the results of Lee and the second named author. We exclude the case of the Kodaira dimension $κ(W)=1$ when the number $k$ of isolated fixed points of an involution $σ$ on $S$ is nine. The possibilities of branch divisors $B_0$ are reduced for the case $k=9$, and are newly given for the case $k=11$. Moreover, we show that if the branch divisor $B_0$ has three irreducible components, then $S$ is an Inoue surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smooth minimal surfaces of general type with $p_g=0, K^2=7$ and involutions Chen, Yifan Shin, YongJoo Zhang, Han Algebraic Geometry 14J29 Lee and the second named author studied involutions on smooth minimal surfaces $S$ of general type with $p_g(S)=0$ and $K_S^2=7$. They gave the possibilities of the birational models $W$ of the quotients and the branch divisors $B_0$ induced by involutions $σ$ on the surfaces $S$. In this paper we improve and refine the results of Lee and the second named author. We exclude the case of the Kodaira dimension $κ(W)=1$ when the number $k$ of isolated fixed points of an involution $σ$ on $S$ is nine. The possibilities of branch divisors $B_0$ are reduced for the case $k=9$, and are newly given for the case $k=11$. Moreover, we show that if the branch divisor $B_0$ has three irreducible components, then $S$ is an Inoue surface. |
| title | Smooth minimal surfaces of general type with $p_g=0, K^2=7$ and involutions |
| topic | Algebraic Geometry 14J29 |
| url | https://arxiv.org/abs/2507.01405 |