Czechoslovak Mathematical Journal, Vol. 69, No. 4, pp. 1061-1068, 2019


On the generalized vanishing conjecture

Zhenzhen Feng, Xiaosong Sun

Received January 26, 2018.   Published online May 24, 2019.

Abstract:  We show that the GVC (generalized vanishing conjecture) holds for the differential operator $\Lambda=(\partial_x-\Phi(\partial_y))\partial_y$ and all polynomials $P(x,y)$, where $\Phi(t)$ is any polynomial over the base field. The GVC arose from the study of the Jacobian conjecture.
Keywords:  Jacobian conjecture; generalized vanishing conjecture; differential operator
Classification MSC:  14R15, 13N15


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Affiliations:   Zhenzhen Feng, Xiaosong Sun (corresponding author), School of Mathematics, Jilin University, Qianjin Street, Changchun 130012, China, e-mail: fengzz13@mails.jlu.edu.cn, sunxs@jlu.edu.cn


 
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