Pinchuk maps, function fields, and real Jacobian conjectures

Details Pinchuk maps, function fields, and real Jacobian conjectures Pinchuk maps, function fields, and real Jacobian conjectures

2012-02-14

arxiv.org/abs/1202.2949v2

Mathematics

Algebraic Geometry

1 illustration, 36 pages; v2 corrects R(T) equation in the appendix, with consequent revisions to the remainder of the appendi

Scientific paper

All counterexamples of Pinchuk type to the strong real Jacobian conjecture (SRJC) are shown to have function field extensions of degree six with no nontrivial automorphisms. Real Jacobian conjectures are considered for rational, as well as polynomial, maps, with nonrational inverses allowed in both cases. The birational and Galois cases are highlighted. Modifications, in particular to the SRJC, that exclude the Pinchuk counterexamples, are suggested.

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