Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2010; 47(1): 211-219

Printed January 1, 2010

https://doi.org/10.4134/BKMS.2010.47.1.211

Copyright © The Korean Mathematical Society.

A polar, the class and plane Jacobian conjecture

Dosang Joe

Konkuk University

Abstract

Let $P$ be a Jacobian polynomial such as $\deg P=\deg_y P$. Suppose the Jacobian polynomial $P$ satisfies the intersection condition satisfying $\dim_{\mathbb C} \mathbb C[x,y]/\langle P, P_y\rangle=\deg P-1$, we can prove that the Keller map which has $P$ as one of coordinate polynomial always has its inverse.

Keywords: polar, class of plane curve, plane Jacobian conjecture

MSC numbers: Primary 32S55; Secondary 14H20

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