A geometric approach to the Jacobian Conjecture in ℂ²

Ludwik M. Drużkowski

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 95-101
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Ludwik M. Drużkowski. "A geometric approach to the Jacobian Conjecture in ℂ²." Annales Polonici Mathematici 55.1 (1991): 95-101. <http://eudml.org/doc/262260>.

@article{LudwikM1991,
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.},
author = {Ludwik M. Drużkowski},
journal = {Annales Polonici Mathematici},
keywords = {Jacobian conjecture; Riemann-Hurwitz-relation},
language = {eng},
number = {1},
pages = {95-101},
title = {A geometric approach to the Jacobian Conjecture in ℂ²},
url = {http://eudml.org/doc/262260},
volume = {55},
year = {1991},
}

TY - JOUR
AU - Ludwik M. Drużkowski
TI - A geometric approach to the Jacobian Conjecture in ℂ²
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 95
EP - 101
AB - 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.
LA - eng
KW - Jacobian conjecture; Riemann-Hurwitz-relation
UR - http://eudml.org/doc/262260
ER -

References

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