A note on the kernel of a locally nilpotent derivation
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- by Gene Freudenburg PDF
- Proc. Amer. Math. Soc. 124 (1996), 27-29 Request permission
Abstract:
This note concerns locally nilpotent derivations $D$ of the polynomial ring $\mathbf C[X_1,\dots , X_n]$. It is shown that if $D$ annihilates a polynomial in two variables, then $D$ annihilates a variable.References
- Rudolf Rentschler, Opérations du groupe additif sur le plan affine, C. R. Acad. Sci. Paris Sér. A-B 267 (1968), A384–A387 (French). MR 232770
- I. R. Shafarevich, Osnovy algebraicheskoĭ geometrii. Tom 1, 2nd ed., “Nauka”, Moscow, 1988 (Russian). Algebraicheskie mnogoobraziya v proektivnom prostranstve. [Algebraic varieties in projective space]. MR 969372
- Dennis M. Snow, Unipotent actions on affine space, Topological methods in algebraic transformation groups (New Brunswick, NJ, 1988) Progr. Math., vol. 80, Birkhäuser Boston, Boston, MA, 1989, pp. 165–176. MR 1040863
Additional Information
- Gene Freudenburg
- Affiliation: Department of Mathematical Sciences, Ball State University, Muncie, Indiana 47306
- Address at time of publication: Department of Mathematics, University of Southern Indiana, Evansville, Indiana 47712
- Received by editor(s): June 6, 1994
- Received by editor(s) in revised form: July 15, 1994
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 27-29
- MSC (1991): Primary 13B25; Secondary 14L30
- DOI: https://doi.org/10.1090/S0002-9939-96-03003-1
- MathSciNet review: 1285990