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THE FACTORIAL CONJECTURE AND IMAGES OF LOCALLY NILPOTENT DERIVATIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 101 / Issue 1 / February 2020
- Published online by Cambridge University Press:
- 20 May 2019, pp. 71-79
- Print publication:
- February 2020
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- Article
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The factorial conjecture was proposed by van den Essen et al. [‘On the image conjecture’, J. Algebra 340(1) (2011), 211–224] to study the image conjecture, which arose from the Jacobian conjecture. We show that the factorial conjecture holds for all homogeneous polynomials in two variables. We also give a variation of the result and use it to show that the image of any linear locally nilpotent derivation of
$\mathbb{C}[x,y,z]$ is a Mathieu–Zhao subspace.
