JP Journal of Algebra, Number Theory and Applications
Volume 36, Issue 3, Pages 269 - 277
(June 2015) http://dx.doi.org/10.17654/JPANTAJun2015_269_277 |
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POINCARÉ SERIES OF NON-DIVISORIAL VALUATIONS ON TWO-DIMENSIONAL FUNCTION FIELDS
Charles Li and Hans Schoutens
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Abstract: We use dual graphs and generating sequences of valuations to compute the Poincaré series of non-divisorial valuations on function fields of dimension two. The Poincaré series are shown to reflect data from the dual graphs and hence carry equivalent information. This extends Galindo’s earlier results on the Poincaré series of divisorial valuations and consequently offers an alternative classification of valuations via Poincaré series. |
Keywords and phrases: Poincaré series, dual graphs of valuations, valuation theory. |
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