Bifurcation locus and branches at infinity of a polynomial f : C2 -> C

Mihai Tibar (1) , Zbigniew Jelonek (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 Institut de Mathématiques, Académie des Sciences de Pologne

We show that the number of bifurcation points at infinity of a polynomial function f : C2 -> C is at most the number of branches at infinity of a generic fiber of f and that this upper bound can be diminished by one in certain cases.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Mihai Tibar, Zbigniew Jelonek. Bifurcation locus and branches at infinity of a polynomial f : C2 -> C. Mathematische Annalen, 2015, 361 ( 3-4), pp.1049-1054. ⟨hal-01253323⟩