与完全退化曲线相关的二次曲线
Conics associated with totally degenerate curves
摘要：
设$k$为字段。设$X/k$是稳定曲线，其几何不可约分支是光滑的有理曲线.对它的正规化进行Stein分解，得到一条二次曲线。我们证明了圆锥曲线在某些情况下是不可裂的。作为应用，我们证明了对于$g\geq3$，普适亏格$g$曲线的周期和指数都等于$2g-2$ .
英文摘要：
Let $k$ be a field. Let $X/k$ be a stable curve whose geometric irreducible components are smooth rational curves. Taking Stein factorization of its normalization, we get a conic. We show the conic is non-split in certain cases. As an application, we show for $g\geq3$, the period and index of the universal genus $g$ curve both equal to $2g-2$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
