On the classification of product-quotient surfaces with $q=0$, $p_g=3$ and their canonical map
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909193787670528 |
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| author | Fallucca, Federico |
| author_facet | Fallucca, Federico |
| contents | In this work we present new results to produce an algorithm that returns, for any fixed pair of natural integers $K^2$ and $χ$, all regular surfaces $S$ of general type with self-intersection $K_S^2=K^2$ and Euler characteristic $χ(\mathcal O_S)=χ$, that are product-quotient surfaces. The key result we obtain is an algebraic characterization of all families of regular product-quotients surfaces, up to isomorphism, arising from a pair of $G$-coverings of $\mathbb P^1$. As a consequence of our work, we provide a classification of all regular product-quotient surfaces of general type with $23\leq K^2\leq 32$ and $χ(\mathcal O_S)=4$. Furthermore, we study their canonical map and present several new examples of surfaces of general type with a high degree of the canonical map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04425 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the classification of product-quotient surfaces with $q=0$, $p_g=3$ and their canonical map Fallucca, Federico Algebraic Geometry Group Theory In this work we present new results to produce an algorithm that returns, for any fixed pair of natural integers $K^2$ and $χ$, all regular surfaces $S$ of general type with self-intersection $K_S^2=K^2$ and Euler characteristic $χ(\mathcal O_S)=χ$, that are product-quotient surfaces. The key result we obtain is an algebraic characterization of all families of regular product-quotients surfaces, up to isomorphism, arising from a pair of $G$-coverings of $\mathbb P^1$. As a consequence of our work, we provide a classification of all regular product-quotient surfaces of general type with $23\leq K^2\leq 32$ and $χ(\mathcal O_S)=4$. Furthermore, we study their canonical map and present several new examples of surfaces of general type with a high degree of the canonical map. |
| title | On the classification of product-quotient surfaces with $q=0$, $p_g=3$ and their canonical map |
| topic | Algebraic Geometry Group Theory |
| url | https://arxiv.org/abs/2405.04425 |