Bifurcation set of multi-parameter families of complex curves

Abstract

The problem of detecting the bifurcation set of polynomial mappings ${\mathbb{C}}^m\to {\mathbb{C}}^k$, $m\ge 2$, $m\ge k\ge 1$, 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 fibres. We provide a complete answer to the general case $m=k+1\ge 3$ in terms of the Betti numbers of fibres and of a vanishing phenomenon discovered in the late 1990s in the real setting.

same content, small corrections, new presentation. Accepted by the Journal of Topology

Cited by in corpus (2)

• Global index of real polynomials
• On Topological Approaches to the Jacobian Conjecture in ${\mathbb{C}}^n$