Open Access
March 2012 Tame and wild degree functions
Daniel Daigle
Osaka J. Math. 49(1): 53-80 (March 2012).


We give examples of degree functions $\deg\colon R \to M \cup \{-\infty\}$, where $R$ is $\mathbb{C}[X,Y]$ or $\mathbb{C}[X,Y,Z]$ and $M$ is $\mathbb{Z}$ or $\mathbb{N}$, whose behaviour with respect to $\mathbb{C}$-derivations $D\colon R \to R$ is pathological in the sense that $\{\deg(Dx) - \deg(x) \mid x \in R\setminus \{0\}\}$ is not bounded above. We also give several general results stating that such pathologies do not occur when the degree functions satisfy certain hypotheses.


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Daniel Daigle. "Tame and wild degree functions." Osaka J. Math. 49 (1) 53 - 80, March 2012.


Published: March 2012
First available in Project Euclid: 21 March 2012

zbMATH: 1261.14035
MathSciNet: MR2903254

Primary: 14R20
Secondary: 12J20 , 13A18 , 13N15

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

Vol.49 • No. 1 • March 2012
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