AI 中文总结
研究德利涅-芒福德栈上由Yu方法定义的非正则霍奇滤子，证明其不依赖紧化，该结果适用于Harder和Lee的orbifold非正则霍奇数研究，仅依赖栈Landau–Ginzburg模型。
AI 中文摘要
设(𝒰,w)是ℂ上有限型的光滑分离德利涅-芒福德栈，带有正则函数w。遵循Yu的方法，可利用紧化在其扭曲 de Rham 上同调上定义一个滤子，该紧化还给出计算此滤子的Kontsevich格。w在紧化上的延拓可能仅为有理的，仅要求在极点除子附近满足局部非退化条件。我们证明所得滤子不依赖于紧化，证明采用良分解与栈弱因子分解，将比较归结为边界除子上的爆破与根，对两种运算均建立了Yu复形与Kontsevich复形的滤子比较定理。Harder和Lee在研究栈Clarke镜像对时用到了orbifold非正则霍奇数，紧化独立性在其设定下逐分支适用，因此所得orbifold滤子与非正则霍奇数仅依赖于栈Landau–Ginzburg模型。
英文摘要
Let $(\mathscr U,w)$ be a smooth separated Deligne--Mumford stack of finite type over $\mathbb C$, with a regular function $w$. Following Yu, one can use a compactification to define a filtration on its twisted de Rham cohomology. The same compactification gives Kontsevich lattices that compute this filtration. The extension of $w$ on the compactification may be only rational. Only a local nondegeneracy condition near the polar divisor is imposed. We prove that the resulting filtration does not depend on the compactification. The proof uses good resolutions and stacky weak factorization. This reduces the comparison to blowups and roots along boundary divisors. Filtered comparison theorems for the Yu and Kontsevich complexes are established for both operations. Harder and Lee use orbifold irregular Hodge numbers in their study of stacky Clarke mirror pairs. Compactification independence applies sector by sector to their setting. Thus the resulting orbifold filtration and irregular Hodge numbers depend only on the stack Landau--Ginzburg model.
Comments37 pages. Substantially revised version; notation standardized, arguments and exposition clarified
