Polynomial complements
A covering is said to be polynomial [\textit{V. L. Hansen}, J. Reine Angew. Math. 314, 29-39 (1980; Zbl 0421.57001)] if it admits an embedding, over the base space, into the trivial complex line bundle. The complement of an n-fold polynomial covering is a locally trivial fibre bundle whose fibres are planes with n points removed. It is shown that equivalence classes of such complement fibrations are in bijective correspondence with principal B(n)-bundles, where B(n) is the braid group on n strings.
complement of an n-fold polynomial covering
scientific article; zbMATH DE number 4090371