论文标题
基本消失周期的管类
Tube classes over elementary vanishing cycles
论文作者
论文摘要
令$ x $为封闭的Riemann表面。当$ x $嵌入投影空间中时，可以通过C. schnell的管映射从其光滑的超平面切片家族中的单一型中获得第一个理性的共同体学组。我们通过将管子映射与拓扑亚伯 - 雅各比映射联系起来，将此结果推广到第一个积分同源组。通过利用映射类组的操作，我们证明了从基本消失的周期构建的所有管类构成的所有管构成了$ x $的第一个积分同源组的cofinite子组。
Let $X$ be a closed Riemann surface. When $X$ is embedded into a projective space, the first rational cohomology group can be concretely obtained from the monodromy in the family of its smooth hyperplane sections by C. Schnell's tube mapping. We generalize this result to the first integral homology group by relating the tube mapping with the topological Abel--Jacobi mapping. By making use of the mapping class group action, we prove that all tube classes constructed from the elementary vanishing cycles form a cofinite subgroup of the first integral homology group of $X$.
