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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.

 

 

 

 

 

 

 

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