A local Zariski-van Kampen theorem
Helmut A. Hamm
Journal of Singularities
volume 30 (2026), 216-241
Received: 8 August 2025. In revised form: 13 May 2026
Abstract:
The term "Zariski-van Kampen theorem" refers to results which allow to compute homology (or homotopy) groups of smooth quasi-projective varieties, comparing with a general hyperplane section. Here we concentrate on the local analogue and prove a corresponding theorem not only for homology but also for homotopy groups. This paves at the same time the way to complete the treatment of the global case.
2020 Mathematical Subject Classification:
32S05, 32S50
Key words and phrases:
Zariski-van Kampen, variation, open book decomposition, nearby fibre
Author(s) information:
Helmut A. Hamm
Mathematisches Institut
Universität Münster
Einsteinstrasse 62
48149 Münster, Germany
email: hamm@uni-muenster.de