, Volume 32, Issue 2-3, pp 97-106

Polynomial maps with constant Jacobian

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Abstract

It has been long conjectured that ifn polynomialsf 1, …,f n inn variables have a (non-zero) constant Jacobian determinant then every polynomial can be expressed as a polynomial inf 1, …,f n. In this paper, various extra assumptions (particularly whenn=2) are shown to imply the conclusion. These conditions are discussed algebraically and geometrically.