发表机构
The University of Manchester（曼彻斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究A型局部完全交舒伯特簇，证明接触刚性定理，并给出奇异轨迹为单光滑分量时的比较核与Kazhdan-Lusztig多项式显式公式。
AI 中文摘要
设$X_w$为A型局部完全交舒伯特簇。我们证明了接触刚性：存在两个光滑奇异分量迫使某对奇异分量在各自中包含一个余维数为一的公共舒伯特子簇。若奇异轨迹为单个光滑分量$X_z$，则有理比较核为$IC_z$，且对所有$u\leq z$有$P_{u,w}(q)=1+q^{(\ell(w)-\ell(z)-1)/2}$。第一个证明将模式回避与计算机辅助的有限重叠分类、矩形继承和极值修复相结合。第二个证明建立了Woo定理的假设，并利用欧拉示性数和Bruhat三角性来识别整个周遍核。
英文摘要
Let $X_w$ be a Type A local complete intersection Schubert variety. We prove Contact Rigidity: the existence of two smooth singular components forces some pair of singular components to contain a common Schubert subvariety of codimension one in each. If the singular locus is a single smooth component $X_z$, the rational comparison kernel is $IC_z$, and $P_{u,w}(q)=1+q^{(\ell(w)-\ell(z)-1)/2}$ for every $u\leq z$. The first proof combines pattern avoidance with a computer-assisted finite overlap classification, rectangle inheritance, and extremal repairs. The second establishes the hypotheses of Woo's theorem and uses Euler characteristics and Bruhat triangularity to identify the entire perverse kernel.
Comments30 pages, 4 figures. Python verification code and recorded output included as ancillary files
