On the Poincaré polynomial of a complement of hyperplanes
Consider the Poincaré polynomial \[ Poin(Y;t)=\sum_{i=1}^n t^i \dim_{\mathbb C} H^i(Y,\mathbb C), \] where \(Y=\mathbb C^n \setminus \bigcup_I A_I\) is the complement of a union of hyperplanes. The first goal of the paper is to find natural geometric conditions for the Poincaré polynomial to be factorizable over \(\mathbb Z\). The second goal is to identify the coefficients of polynomial divisors of \(Poin(Y;t)\) with some characteristic numbers.
scientific article; zbMATH DE number 1117487
scientific article