论文标题
高椭圆形奇数覆盖物
Hyperelliptic odd coverings
论文作者
论文摘要
我们调查了一类奇数（后果）覆盖物$ c \ to \ to \ m athbb {p}^1 $其中$ c $是高elliptic的，其weierstrass点映射到$ \ mathbb {p}^1 $的一个固定点，并且覆盖率映射使$ c $ culs的超elliptiptic cum cuns in Mathbb $ \ althbb} $ \ p}^p}^p}。我们表明，当$ c $是一般的时候，最小值$ 4G $ 4G $ 4G $ 4G $ 4G $ 4G $ as 4g $ as $ 4g $ as $ 4g $的总数是$ 4G $是$ 4G $，当我们的研究是从三个主要角度进行的：如果固定固定的有效theta特征是固定的，则将其描述为某种类别的微分方程的解决方案；然后，从单型观点和导致最终计算的变形参数中对它们进行了研究。
We investigate a class of odd (ramification) coverings $C \to \mathbb{P}^1$ where $C$ is hyperelliptic, its Weierstrass points maps to one fixed point of $\mathbb{P}^1$ and the covering map makes the hyperelliptic involution of $C$ commute with an involution of $\mathbb{P}^1$. We show that the total number of hyperelliptic odd coverings of minimal degree $4g$ is ${3g \choose g-1} 2^{2g}$ when $C$ is general. Our study is approached from three main perspectives: if a fixed effective theta characteristic is fixed they are described as a solution of a certain class of differential equations; then they are studied from the monodromy viewpoint and a deformation argument that leads to the final computation.
