Home

 

Recent Issues

Volume 52

1

2

3

4

Volume 51

1

2

3

4

Volume 50

1

2

3

4

Volume 49

1

2

3

4

Volume 48

1

2

3

4

Past Issues

 

The Journal

Cover

Aims and Scope

Subscription Information

Editorial Board

Instructions for Author

Contact Us

 

 

 

 

Vietnam Journal of Mathematics 37:1 (2009) 113-125

A Condition for the Properness of Polynomial Maps

Nguyen Thi Thao

Abstract.  In this paper we present a condition for a polynomial map F:= (f1, f2, ..., fn): Rn --->Rn to be a global polynomial diffeomorphism. To do this we express a sufficient condition in terms of the Newton polyhedron for a polynomial function f: Rn  ---> R to be a proper map. We also prove that the fiber f -1(A), with large value |A|, of a proper polynomial f is diffeomorphic to the unit sphere Sn-1, if it is non-empty.

Keywords: Diffeomorphisms, proper maps, Newton polyhedra.

 

 

 

 

 

 

 

Established by Vietnam Academy of Science and Technology & Vietnam Mathematical Society

Published by Springer since January 2013