Non-zero constant Jacobian polynomial maps of ℂ ²

Nguyen Van Chau

Annales Polonici Mathematici (1999)

  • Volume: 71, Issue: 3, page 287-310
  • ISSN: 0066-2216

Abstract

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We study the behavior at infinity of non-zero constant Jacobian polynomial maps f = (P,Q) in ℂ² by analyzing the influence of the Jacobian condition on the structure of Newton-Puiseux expansions of branches at infinity of level sets of the components. One of the results obtained states that the Jacobian conjecture in ℂ² is true if the Jacobian condition ensures that the restriction of Q to the curve P = 0 has only one pole.

How to cite

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Nguyen Van Chau. "Non-zero constant Jacobian polynomial maps of $ℂ²$." Annales Polonici Mathematici 71.3 (1999): 287-310. <http://eudml.org/doc/262821>.

@article{NguyenVanChau1999,
abstract = {We study the behavior at infinity of non-zero constant Jacobian polynomial maps f = (P,Q) in ℂ² by analyzing the influence of the Jacobian condition on the structure of Newton-Puiseux expansions of branches at infinity of level sets of the components. One of the results obtained states that the Jacobian conjecture in ℂ² is true if the Jacobian condition ensures that the restriction of Q to the curve P = 0 has only one pole.},
author = {Nguyen Van Chau},
journal = {Annales Polonici Mathematici},
keywords = {Jacobian conjecture; polynomial automorphism; Newton-Puiseux expansion; Newton-Puiseux expansions},
language = {eng},
number = {3},
pages = {287-310},
title = {Non-zero constant Jacobian polynomial maps of $ℂ²$},
url = {http://eudml.org/doc/262821},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Nguyen Van Chau
TI - Non-zero constant Jacobian polynomial maps of $ℂ²$
JO - Annales Polonici Mathematici
PY - 1999
VL - 71
IS - 3
SP - 287
EP - 310
AB - We study the behavior at infinity of non-zero constant Jacobian polynomial maps f = (P,Q) in ℂ² by analyzing the influence of the Jacobian condition on the structure of Newton-Puiseux expansions of branches at infinity of level sets of the components. One of the results obtained states that the Jacobian conjecture in ℂ² is true if the Jacobian condition ensures that the restriction of Q to the curve P = 0 has only one pole.
LA - eng
KW - Jacobian conjecture; polynomial automorphism; Newton-Puiseux expansion; Newton-Puiseux expansions
UR - http://eudml.org/doc/262821
ER -

References

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