Poincare Series of Non-divisorial Valuations on Two-dimensional Function Fields

2015/04/22 by Li, Charles, Schoutens, Hans
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.05656

Abstract

We use dual graphs and generating sequences of valuations to compute the Poincare series of non-divisorial valuations on function fields of dimension two. The Poincare series are shown to reflect data from the dual graphs and hence carry equivalent information. This extends Galindo's earlier results on the Poincare series of divisorial valuations and consequently offers an alternative classification of valuations via Poincare series.

Related

• Dual Graphs and Generating Sequences of Non-divisorial Valuations on Two-dimensional Function Fields
• Poincaré series of valuations on functions over a field
• Real Poincaré series of a plane divisorial valuation
• The Poincare series of divisorial valuations in the plane defines the topology of the set of divisors
• Generating sequences and Poincaré series for a finite set of plane divisorial valuations