接触轨迹的上同调
代数几何
2023-08-25 v3
摘要
我们构造了一个收敛于复多项式第 m 个接触轨迹的紧支上同调的谱序列。其第一页通过对数分解显式描述，并在多项式具有孤立奇点时，与收敛于单值性第 m 次迭代的 Floer 上同调的 McLean 谱序列的第一页一致。受此联系的启发，我们猜想：若两个全纯函数芽是嵌入拓扑等价的，则其切锥的 Milnor 纤维同伦等价。
引用
@article{arxiv.1911.08213,
title = {Cohomology of contact loci},
author = {Nero Budur and Javier Fernández de Bobadilla and Quy Thuong Lê and Hong Duc Nguyen},
journal= {arXiv preprint arXiv:1911.08213},
year = {2023}
}
备注
Correction: Prop. 1.2 is false: if the ample divisor W is replaced by eW with e>d, the new spectral sequence has zero differentials for the first e pages. The last sentence of the proof of Prop. 1.2 is not true. Prop 1.2 does not affect the rest of the paper