A note on the plane Jacobian conjecture

Volume 105 / 2012

Nguyen Van Chau 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.

Authors

  • Nguyen Van ChauInstitute of Mathematics
    Vietnam Academy of Science and Technology
    18 Hoang Quoc Viet
    10307 Hanoi,Vietnam
    e-mail

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