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Contact Rigidity and Comparison Kernels for Type A lci Schubert Varieties

  • Minghua Dou
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Abstract

Let Xw 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 Xz, the rational comparison kernel is ICz, and Pu,w(q)=1+q(ℓ(w)−ℓ(z)−1)/2 for every u≤ 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.

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Cite

BibTeXRIS
BibTeX
@misc{dou2026contact,
  title = {{Contact Rigidity and Comparison Kernels for Type A lci Schubert Varieties}},
  author = {Minghua Dou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13835},
  eprint = {2609.13835},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13835},
}
RIS
TY  - UNPB
TI  - Contact Rigidity and Comparison Kernels for Type A lci Schubert Varieties
AU  - Minghua Dou
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13835
UR  - https://arxiv.org/abs/2609.13835
AB  - 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^(ℓ(w)−ℓ(z)−1)/2 for every u≤ 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.
ER  -