Hessenberg理想纤维的仿射铺砌
代数几何
2024-06-28 v4 表示论
摘要
我们定义旗簇的某些闭子簇，即Hessenberg理想纤维，并证明它们可由仿射空间铺砌。Hessenberg理想纤维是Springer纤维的自然推广。在型中，我们给出所有Hessenberg理想纤维的显式描述，研究它们的一些几何性质，并利用它们完全分类Tymoczko关于Weyl群在正则半单Hessenberg簇上同调中的点作用。
引用
@article{arxiv.2007.08712,
title = {Affine Pavings of Hessenberg Ideal Fibers},
author = {Ke Xue},
journal= {arXiv preprint arXiv:2007.08712},
year = {2024}
}
备注
[v4] adds recent related works and citations of this paper. [v3] improves Lemma 2.5 to a new version that achieves the same result from a weaker assumption. Proposition 2.13 is remade to show that Lemma 2.5 still applies to $\mathcal{O}_v$ even though it is not necessarily a vector bundle over $\mathcal{O}_v^{\lambda}$. [v2] added an accidentally omitted case of $U$ for type $F_4$ in section 6