Geodesic
Note on the Jacobian condition and the non-proper value set
Nguyen Van Chau1
1 Hanoi Institute of Mathematics 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam
Annales Polonici Mathematici, Tome 84 (2004) no. 3, pp. 203-210

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that the non-proper value set of a polynomial map $(P,Q): {{\mathbb C}}^2\rightarrow {{\mathbb C}}^2$ satisfying the Jacobian condition $\mathop {\rm det}D(P,Q)\equiv {\rm const}\not =0$, if non-empty, must be a plane curve with one point at infinity.
DOI : 10.4064/ap84-3-2
Keywords: non proper value set polynomial map mathbb rightarrow mathbb satisfying jacobian condition mathop det equiv const non empty plane curve point infinity

Nguyen Van Chau 1

1 Hanoi Institute of Mathematics 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam 
@article{10_4064_ap84_3_2,
     author = {Nguyen Van Chau},
     title = {Note on the {Jacobian} condition and the
 non-proper value set},
     journal = {Annales Polonici Mathematici},
     pages = {203--210},
     publisher = {mathdoc},
     volume = {84},
     number = {3},
     year = {2004},
     doi = {10.4064/ap84-3-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap84-3-2/}
}
TY  - JOUR
AU  - Nguyen Van Chau
TI  - Note on the Jacobian condition and the
 non-proper value set
JO  - Annales Polonici Mathematici
PY  - 2004
SP  - 203
EP  - 210
VL  - 84
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap84-3-2/
DO  - 10.4064/ap84-3-2
LA  - en
ID  - 10_4064_ap84_3_2
ER  - 
%0 Journal Article
%A Nguyen Van Chau
%T Note on the Jacobian condition and the
 non-proper value set
%J Annales Polonici Mathematici
%D 2004
%P 203-210
%V 84
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap84-3-2/
%R 10.4064/ap84-3-2
%G en
%F 10_4064_ap84_3_2
Nguyen Van Chau. Note on the Jacobian condition and the
 non-proper value set. Annales Polonici Mathematici, Tome 84 (2004) no. 3, pp. 203-210. doi: 10.4064/ap84-3-2

Cité par Sources :