Tame and wild degree functions

Details Tame and wild degree functions Tame and wild degree functions

2010-07-03

arxiv.org/abs/1007.0508v1

Mathematics

Algebraic Geometry

25 pages

Scientific paper

We give examples of degree functions deg : R --> M, where R is a polynomial ring in 2 or 3 variables and M is either the integers or the natural numbers, whose behaviour with respect to derivations D : R --> R is pathological in the sense that deg(Dx) - deg(x) (where x in R \ {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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