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# A Note on Locally Nilpotent Derivations\\ and Variables of $k[X,Y,Z]$

Published:2009-12-01
Printed: Dec 2009
• Daniel Daigle
• Shulim Kaliman
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## Abstract

We strengthen certain results concerning actions of $(\Comp,+)$ on $\Comp^{3}$ and embeddings of $\Comp^{2}$ in $\Comp^{3}$, and show that these results are in fact valid over any field of characteristic zero.
 Keywords: locally nilpotent derivations, group actions, polynomial automorphisms, variable, affine space
 MSC Classifications: 14R10 - Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) 14R20 - Group actions on affine varieties [See also 13A50, 14L30] 14R25 - Affine fibrations [See also 14D06] 13N15 - Derivations