Pencil of irreducible rational curves and Plane Jacobian conjecture

Details Pencil of irreducible rational curves and Plane Jacobian conjecture Pencil of irreducible rational curves and Plane Jacobian conjecture

2009-05-25

arxiv.org/abs/0905.3939v3

Mathematics

Algebraic Geometry

Correct main result and tittle

Scientific paper

We are concerned with the behavior of the polynomial maps $F=(P,Q)$ of
$\mathbb{C}^2$ with finite fibres and satisfying the condition that all of the
curves $aP+bQ=0$, $(a:b)\in \mathbb{P}^1$, are irreducible rational curves. The
obtained result shows that such polynomial maps $F$ is invertible if $(0,0)$ is
a regular value of $F$ or if the Jacobian condition holds.

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