New Proofs for the Abhyankar-Gurjar Inversion Formula and the Equivalence of the Jacobian Conjecture and the Vanishing Conjecture

Details New Proofs for the Abhyankar-Gurjar Inversion Formula and the Equivalence of the Jacobian Conjecture and the Vanishing Conjecture New Proofs for the Abhyankar-Gurjar Inversion Formula and the Equivalence of the Jacobian Conjecture and the Vanishing Conjecture

2009-07-23

arxiv.org/abs/0907.3991v2

Mathematics

Algebraic Geometry

Latex, 18 pages. Following the referee the Introduction and the preliminary part of the paper have been slightly re-written. T

Scientific paper

We first give a new proof and also a new formulation for the Abhyankar-Gurjar inversion formula for formal maps of affine spaces. We then use the reformulated Abhyankar-Gurjar formula to give a more straightforward proof for the equivalence of the Jacobian Conjecture with a special case of the Vanishing Conjecture of (homogeneous) quadratic differential operators with constant coefficients.

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