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New proofs for the Abhyankar-Gurjar inversion formula and the equivalence of the Jacobian conjecture and the vanishing conjecture


Author: Wenhua Zhao
Journal: Proc. Amer. Math. Soc. 139 (2011), 3141-3154
MSC (2010): Primary 14R15, 32W99, 14R10
DOI: https://doi.org/10.1090/S0002-9939-2011-10744-5
Published electronically: January 26, 2011
MathSciNet review: 2811269
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Abstract: 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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Additional Information

Wenhua Zhao
Affiliation: Department of Mathematics, Illinois State University, Normal, Illinois 61790-4520
Email: wzhao@ilstu.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-10744-5
Keywords: The Abhyankar-Gurjar inversion formula, the Jacobian conjecture, the vanishing conjecture of quadratic differential operators
Received by editor(s): July 23, 2009
Received by editor(s) in revised form: August 17, 2010
Published electronically: January 26, 2011
Additional Notes: The author has been partially supported by NSA Grant H98230-10-1-0168
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.