A note on the plane Jacobian conjecture
Volume 105 / 2012
Annales Polonici Mathematici 105 (2012), 13-19
MSC: Primary 14R15, 14R10; Secondary 14R25, 14D06.
DOI: 10.4064/ap105-1-2
Abstract
It is shown that every polynomial function $P:\mathbb{C}^2\to\mathbb{C}$ with irreducible fibres of the same genus must be a coordinate. Consequently, there do not exist counterexamples $F=(P,Q)$ to the Jacobian conjecture such that all fibres of $P$ are irreducible curves with the same genus.
