发表机构
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明固定极点阶数的 Deligne--Mumford Landau--Ginzburg 族中非正则 Hodge 滤过构成滤过代数向量丛，并满足平移 Griffiths 横截性，进而应用于环面栈，表明滤过与分次维数不依赖系数，且可由组合复形计算。
AI 中文摘要
我们证明，在具有固定极点阶数的 Deligne--Mumford Landau--Ginzburg 模型的光滑族中，典范非正则 Hodge 滤过可组装成滤过代数向量丛。更精确地，扭曲 de Rham 上同调构成一个携带典范代数可积连接的向量丛，每个有理非正则 Hodge 层都是具有局部自由商的子丛，且每个有理分次片都是向量丛。这些构造与任意有限型基变换可交换，且连接满足平移 Griffiths 横截性。因此，所有滤过维数和分次维数都是局部常数。作为应用，对于光滑拟射影环面 Deligne--Mumford 栈以及满足支撑条件的每个固定无穷远 Newton 多面体，这些结论在 Laurent 多项式的完整系数轨迹上成立，其中 Laurent 多项式在无穷远处非退化。特别地，其滤过维数和分次维数与系数无关。当所得栈扇构成 Clarke 对偶对时，非正则 Hodge 数由 Harder--Lee 的组合 $\Xi$-复形计算。
英文摘要
We prove that the canonical irregular Hodge filtrations in smooth families of Deligne--Mumford Landau--Ginzburg models with fixed pole orders assemble into filtered algebraic vector bundles. More precisely, twisted de Rham cohomology forms a vector bundle carrying a canonical algebraic integrable connection, every rational irregular Hodge level is a subbundle with locally free quotient, and every rational graded piece is a vector bundle. These constructions commute with arbitrary finite-type base change, and the connection satisfies shifted Griffiths transversality. Consequently, all filtered and graded dimensions are locally constant. As an application, for a smooth quasiprojective toric Deligne--Mumford stack and every fixed Newton polytope at infinity satisfying the support condition, these conclusions hold over the full coefficient locus of Laurent polynomials that are nondegenerate at infinity. In particular, their filtered and graded dimensions are independent of the coefficients. When the resulting stacky fans form a Clarke dual pair, the irregular Hodge numbers are computed by Harder--Lee's combinatorial $Ξ$-complex.
