AI 中文总结
本文研究 Hodge 模空间中 Simpson 层的闭包关系，证明 Heinloth 权在特化改变固定分量时严格增加，并构造反例反驳 Simpson 嵌套猜想，同时从 $\Theta$ 分层角度讨论 Simpson 滤过。
AI 中文摘要
本文研究亏格 $g\geq2$ 的光滑复射影曲线上 Hodge 模空间中 Simpson 层的闭包关系，并在每个秩下证明：当特化改变固定分量时，Heinloth 权严格增加。对于稳定的全链，我们通过比较相应滤过步骤的次数来细化这一数值条件，并在每个秩 $n\geq4$ 下构造反例，反驳 Dolbeault 与 de Rham 模空间的 Simpson 嵌套猜想。利用该权的极大性质，我们还从 $\Theta$ 分层角度讨论 Simpson 滤过。
英文摘要
In this paper, we study closure relations of Simpson strata in Hodge moduli spaces over a smooth complex projective curve of genus $g\geq2$ and prove in every rank that the Heinloth weight strictly increases whenever a specialization changes the fixed component. For stable full chains, we refine this numerical condition by comparing the degrees of the corresponding filtration steps and construct counterexamples to Simpson's nestedness conjecture for the Dolbeault and de Rham moduli spaces in every rank $n\geq4$. Using the maximum property of this weight, we also discuss Simpson filtrations from the viewpoint of $Θ$ stratifications.
CommentsPreliminary version, 21 pages
