On the generalized vanishing conjecture

Zhenzhen Feng; Xiaosong Sun

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 4, page 1061-1068
  • ISSN: 0011-4642

Abstract

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We show that the GVC (generalized vanishing conjecture) holds for the differential operator Λ = ( ∂ x - Φ ( ∂ y ) ) ∂ y and all polynomials P ( x , y ) , where Φ ( t ) is any polynomial over the base field. The GVC arose from the study of the Jacobian conjecture.

How to cite

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Feng, Zhenzhen, and Sun, Xiaosong. "On the generalized vanishing conjecture." Czechoslovak Mathematical Journal 69.4 (2019): 1061-1068. <http://eudml.org/doc/294692>.

@article{Feng2019,
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.},
author = {Feng, Zhenzhen, Sun, Xiaosong},
journal = {Czechoslovak Mathematical Journal},
keywords = {Jacobian conjecture; generalized vanishing conjecture; differential operator},
language = {eng},
number = {4},
pages = {1061-1068},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the generalized vanishing conjecture},
url = {http://eudml.org/doc/294692},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Feng, Zhenzhen
AU - Sun, Xiaosong
TI - On the generalized vanishing conjecture
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 1061
EP - 1068
AB - 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.
LA - eng
KW - Jacobian conjecture; generalized vanishing conjecture; differential operator
UR - http://eudml.org/doc/294692
ER -

References

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