论文标题
部分可观测时空混沌系统的无模型预测
Degenerations to secant cubic hypersurfaces and limiting Hodge structure
论文作者
论文摘要
Veronese表面的距离品种是一个奇异的立方四倍。单参数退化对此距离立方四倍的hodge结构的退化是B.我们将它们的一些结果推广到Cubic Hyperface是Severi品种的距离品种。具体而言，我们研究了与脱离立方体超表面的一参数退化相关的极限混合Hodge结构。考虑到S.〜USUI对一般权重的Hodge结构的周期结构域的部分压实，我们将极限混合Hodge结构应用于相应的立方体超出面的周期图的局部扩展。
The secant variety of the Veronese surface is a singular cubic fourfold. The degeneration of Hodge structures of one-parameter degenerations to this secant cubic fourfold is a key ingredient for B.~Hassett and R.~Laza in studying the moduli space of cubic fourfolds via the period mapping. We generalize some of their results to the cubic hypersurface that is the secant variety of a Severi variety. Specifically, we study the limit mixed Hodge structures associated to one-parameter degenerations to the secant cubic hypersurface. Considering S.~Usui's partial compactification of a period domain for Hodge structures of general weights, we apply the limit mixed Hodge structure to characterize a local extension of the period map for the corresponding cubic hypersurfaces.
