论文标题
霍奇结构的复杂复杂变化在维度
Degenerating complex variations of Hodge structure in dimension one
论文作者
论文摘要
我们分析了穿刺单元磁盘上Hodge结构的极化复合变化的行为。对于Hodge结构的整体变化，该分析首先由Wilfried Schmid进行。我们摆脱了这样的假设，即单肌转化的特征值是统一的根源。在这种普遍性中，我们为Schmid论文的所有主要结果提供了新的（并且我们认为更概念上的）证明，例如对Hodge Narm的增长率的估计；存在限制混合船体结构的存在； nilpotent轨道定理；以及SL（2） - 轨道定理的简化（但仍然足够强大）的版本。
We analyze the behavior of polarized complex variations of Hodge structure on the punctured unit disk. For integral variations of Hodge structure, this analysis was first carried out by Wilfried Schmid. We get rid of the assumption that the eigenvalues of the monodromy transformation are roots of unity. In this generality, we give new (and, we think, more conceptual) proofs for all the major results in Schmid's paper, such as the estimates for the rate of growth of the Hodge norm; the existence of a limiting mixed Hodge structure; the nilpotent orbit theorem; and a simplified (but still sufficiently powerful) version of the SL(2)-orbit theorem.
