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A note on normal triple covers over $\mathbb{P}^2$ with branch divisors of degree 6
TLDR
In this article, the branch divisor of a normal triple cover over an elliptic curve or a normal cubic surface was shown to be a branch diviser of a regular triple cover.Abstract:
Let $S$ and $T$ be reduced divisors on $\mathbb{P}^2$ which have no common components, and $\Delta=S+2\,T.$ We assume $°\Delta=6.$ Let $\pi:X\to\mathbb{P}^2$ be a normal triple cover with branch divisor $\Delta,$ i.e. $\pi$ is ramified along $S$ (resp. $T$) with the index 2 (resp. 3). In this note, we show that $X$ is either a $\mathbb{P}^1$-bundle over an elliptic curve or a normal cubic surface in $\mathbb{P}^3.$ Consequently, we give a necessary and sufficient condition for $\Delta$ to be the branch divisor of a normal triple cover over $\mathbb{P}^2.$read more
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Covers of algebraic varieties I. A general structure theorem, covers of degree 3,4 and Enriques' surfaces
Gianfranco Casnati,T. Ekedahl +1 more
Proceedings ArticleDOI
A survey on Zariski pairs
TL;DR: The problem of finding the fundamental group of the complement of the given curve (the word complement is understood and often omitted for short) was first considered by Enriques.
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