A geometric approach to the Jacobian Conjecture in ℂ²

Ludwik Drużkowski

ArticleOriginal scientific text

Title

A geometric approach to the Jacobian Conjecture in ℂ²

Authors ¹

Affiliations

Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

We consider polynomial mappings (f,g) of ℂ² with constant nontrivial jacobian. Using the Riemann-Hurwitz relation we prove among other things the following: If g - c (resp. f - c) has at most two branches at infinity for infinitely many numbers c or if f (resp. g) is proper on the level set

g^{- 1} (0)

(resp.

f^{- 1} (0)

), then (f,g) is bijective.

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Title

A geometric approach to the Jacobian Conjecture in ℂ²

Affiliations

Abstract

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