Bifurcation set of multi‐parameter families of complex curves. Issue 3 (22nd June 2018)

• Record Type: Journal Article
• Authors: Joiţa, Cezar; Tibăr, Mihai
• Is Part Of: Journal of topology. Volume 11:Issue 3(2018)
• Page Start: 739
• Page End: 751
• Publication Date: 2018-06-22
• Subjects: 14D06 -- 32S20 (primary) -- 57R45 -- 58K05 -- 58K15 (secondary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12066
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: The problem of detecting the bifurcation set of polynomial mappings C m → C k, m ⩾ 2, m ⩾ k ⩾ 1, has been solved in the case m = 2, k = 1 only. Its solution, which goes back to the 1970s, involves the non‐constancy of the Euler characteristic of fibers. We provide here a complete answer to the general case m = k + 1 ⩾ 3 in terms of the Betti numbers of fibers and of a vanishing phenomenon discovered in the late 1990s in the real setting.