论文标题
lefschetz $（1，1）$的新方法 - 定理
A new approach towards Lefschetz $(1, 1)$-Theorem
论文作者
论文摘要
令$ s $为复杂的投影表面。 Lefschetz最初证明是Lefschetz $（1，1）$ - 定理，通过研究$ S $的超平面段和Abel-Jacobi映射的Lefschetz铅笔。在本文中，我们攻击了lefschetz $（1，1）$ - 定理，通过构建了两次超平面部分的两参数家庭，然后应用拓扑abel-jacobi映射。我们的几何结构将提供一种感应方法，并有一些洞察力，以了解更高维度的情况。我们证明了一个强的管定理，该定理将Schnell的管定理概括为复杂的射击曲线的积分同源组，然后获得Jacobi型反转定理。最后，我们为一般网上的基本消失周期的变形空间提供了几何描述。
Let $S$ be a complex projective surface. Lefschetz originally proved Lefschetz $(1, 1)$--Theorem by studying a Lefschetz pencil of hyperplane sections of $S$ and the Abel--Jacobi mapping. In this paper, we attack Lefschetz $(1, 1)$--Theorem by constructing certain two-parameter families of twice hyperplane sections of $S$ and then applying the topological Abel--Jacobi mapping. Our geometric constructions would give an inductive approach and some insight for higher dimensional cases. We prove a strong tube theorem which generalizes Schnell's tube theorem to integral homology groups for complex projective curves and then obtain a Jacobi-type inversion theorem. In the end, we give a geometric description for the deformation space of an elementary vanishing cycle over a generic net.
