| Autor: |
Hiro-o Tokunaga, Hirotaka Ishida |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009) |
| ISSN: |
0920-1971 |
| DOI: |
10.2969/aspm/05610169 |
| Popis: |
Let $B$ be a reduced sextic curve in $\mathbb{P}^2$. In the case when singularities of $B$ are only six cusps, Zariski proved that there exists a non-Galois triple cover branched at $B$ if and only if $B$ is given by an equation of the form $G_2^3 + G_3^2$, where $G_i$ denotes a homogeneous polynomial of degree $i$. In this article, we generalize Zariski's statement to any reduced sextic curve with at worst simple singularities. To this purpose, we give formulae for numerical invariants of non-Galois triple covers by using Tan's canonical resolution. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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