On Globally Diffeomorphic Polynomial Maps via Newton Polytopes and Circuit Numbers

2016/02/05 by Bajbar, Tomas, Stein, Oliver
#14P99 #26B10 #26C05 #52B20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1602.01977

Abstract

In this article we analyze the global diffeomorphism property of polynomial maps F:ℝⁿ→ℝⁿ by studying the properties of the Newton polytopes at infinity corresponding to the sum of squares polynomials ‖F‖₂². This allows us to identify a class of polynomial maps F for which their global diffeomorphism property on ℝⁿ is equivalent to their Jacobian determinant det JF vanishing nowhere on ℝⁿ. In other words, we identify a class of polynomial maps for which the Real Jacobian Conjecture, which was proven to be false in general, still holds.

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