发表机构
Morningside Center of Mathematics, 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
本文比较无穷远处动机邻近圈与有理紧化上的类，证明开对类与Raibaut紧化无关的动机邻近圈一致，并给出环面证明及Fano-Landau-Ginzburg镜像恒等式的动机-Hodge推导。
AI 中文摘要
我们将无穷远处的动机邻近圈与直接在有理紧化上计算的类进行比较。设$f$是特征零域上光滑簇上的正则函数，$X$是光滑的proper紧化。假设包含边界和$\operatorname{div}_X(f)$的支撑的约化除子在极点附近具有简单正规交叉。我们证明由$1/f$定义的开对类与Raibaut的紧化无关的无穷远处动机邻近圈一致。关键步骤是在横向零极点交点的爆破下的局部消去。对于在无穷远处非退化的Laurent多项式，这一比较给出了Raibaut基本面公式的直接环面证明。等变Hodge实现和加权Ehrhart理论给出保留上同调次数和极限权重过滤的Newton公式，并通过极限-不规则比较确定不规则Hodge数。遗忘权重的特殊化计算具有相同径向支撑的环面堆栈扇的零势弦性不变量，从而得到相应Fano-Landau-Ginzburg镜像恒等式的动机-Hodge推导。在全维弱Fano情形，精细公式将单值特征值和Jordan块大小与惯性年龄和反典范Lefschetz弦识别，给出在$\mathbb C$上的非典范比较。
英文摘要
We compare motivic nearby cycles at infinity with classes computed directly on rational compactifications. Let $f$ be a regular function on a smooth variety over a field of characteristic zero, and let $X$ be a smooth proper compactification. Suppose that a reduced divisor containing the boundary and the support of $\operatorname{div}_X(f)$ has simple normal crossings near the polar locus. We prove that the open-pair class defined by $1/f$ agrees with Raibaut's compactification-independent motivic nearby cycle at infinity. The key step is a local cancellation under blow-ups of transverse zero-pole intersections. For Laurent polynomials nondegenerate at infinity, this comparison yields a direct toric proof of Raibaut's essential-face formula. Equivariant Hodge realization and weighted Ehrhart theory give Newton formulas retaining cohomological degree and the limit-weight filtration, and determine irregular Hodge numbers through the limiting-irregular comparison. The weight-forgetting specialization computes the zero-potential stringy invariant of toric stacky fans with the same radial support, yielding a motivic-Hodge derivation of the corresponding Fano-Landau-Ginzburg mirror identity. In the full-dimensional weak Fano case, the refined formulas identify monodromy eigenvalues and Jordan-block sizes with inertia ages and anticanonical Lefschetz strings, giving a noncanonical comparison over $\mathbb C$.
