A finite morphism $f:X\to \mathbb P^2$ of a a smooth irreducible projective surface $X$ is called an almost generic cover if for each point $p\in \mathbb P^2$ the fibre $f^{-1}(p)$ is supported at least on $deg(f)-2$ distinct points and $f$ is ramified with multiplicity two at a generic point of its ramification locus $R$. In the article, the singular points of the branch curve $B\subset\mathbb P^2$ of an almost generic cover are investigated and main invariants of the covering surface $X$ are calculated in terms of invariants of the curve $B$.

中文翻译：

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在投影平面的几乎通用覆盖上

如果对于每个点 $p\in \mathbb P^2$ 纤维 $f^{，一个光滑的不可约射影表面 $X$ 的有限态射 $f:X\to \mathbb P^2$ 被称为几乎通用的覆盖-1}(p)$ 至少在 $deg(f)-2$ 不同点上得到支持，并且 $f$ 在其分枝轨迹 $R$ 的通用点处以多重性 2 分枝。在文章中，研究了几乎通用的覆盖的分支曲线 $B\subset\mathbb P^2$ 的奇异点，并根据曲线 $B$ 的不变量计算了覆盖面 $X$ 的主要不变量.