Derivations of polynomial algebras without Darboux polynomials

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Abstract

We present several new examples of homogeneous derivations of a polynomial ring k[X]=k[x1,,xn] over a field k of characteristic zero without Darboux polynomials. Using a modification of a result of Shamsuddin, we produce these examples by induction on the number n of variables, thus more easily than the previously known example multidimensional Jouanolou systems of Żoła̧dek.

MSC

Primary
12H05
secondary
13N15

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