New proofs for the Abhyankar-Gurjar inversion formula and the equivalence of the Jacobian conjecture and the vanishing conjecture
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- by Wenhua Zhao PDF
- Proc. Amer. Math. Soc. 139 (2011), 3141-3154 Request permission
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.References
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Additional Information
- Wenhua Zhao
- Affiliation: Department of Mathematics, Illinois State University, Normal, Illinois 61790-4520
- Email: wzhao@ilstu.edu
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2811269