论文标题
通用正常表面奇点的过度椭圆形
Hyperelliptic involutions on generic normal surface singularities
论文作者
论文摘要
在经典的情况下，每个属$ 2 $曲线的平滑代数曲线都是过度的，或者换句话说，它们上有一个完整的线性系列$ G_2^1 $。另一方面，如果$ g> 2 $，则$ 2 $ $ 2 $的普通平滑曲线是非流血的。 在本文中，我们调查了正常表面奇点的情况，因此我们修复了一个分辨率图$ \ MATHCAL {t} $，并从\ cite {nnii}的意义上使用分辨率$ \ tx $的通用奇异性。我们考虑了分辨率$ \ tx $上的整数有效周期$ z $，并研究了完整的线性系列$ g_2^1 $。这篇文章的主要动机是，我们将在下面的手稿中大量使用其结果来计算Abel Maps的图像品种类别。
In the classical case of irreducible smooth algebraic curves every genus $2$ curve is hyperelliptic, or in other words there is a complete linear series $g_2^1$ on them. On the other hand if $g > 2$, then a generic smooth curve of genus $2$ is nonhyperelliptic. In this article we investigate the situation of normal surface singularities, so we fix a resolution graph $\mathcal{T}$ and a generic singularity with resolution $\tX$ corresponding to it in the sense of \cite{NNII}. We consider an integer effective cycle $Z$ on the resolution $\tX$ and investigate the existence of a complete linear series $g_2^1$ on it. The article has the main motivation that we will use heavily the results in it to compute the class of the image varieties of Abel maps in a following manuscript.
