On the Poincaré polynomial of a complement of hyperplanes
type: Item
instance of: scholarly article
title: On the Poincaré polynomial of a complement of hyperplanes
zbMATH Open document ID: 0910.32009
author: Roberto Silvotti
published in: Mathematical Research Letters
publication date: 1999-04-08T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 14F25
zbMATH DE Number: 1117487
zbMATH Keywords: sheaves of logarithmic \(p\)-forms
zbMATH Keywords: arrangement of hyperplanes
zbMATH Keywords: Chern classes
reviewed by: Alexander Mednykh
MaRDI profile type: Publication
DOI: 10.4310/MRL.1997.V4.N5.A3
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description: scientific article; zbMATH DE number 1117487