Arcs and resolution of singularities

2004/02/06 by Johannes Nicaise, Nicaise, Johannes
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0402101

19 pages

arxiv created 2004/02/06 · openalex publication_date 2004/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a certain class of varieties X, we derive a formula for the valuation d_X on the arc space L(Y) of a smooth ambient space Y, in terms of an embedded resolution of singularities. A simple transformation rule yields a formula for the geometric Poincare series. Furthermore, we prove that for this class of varieties, the arithmetic and the geometric Poincare series coincide. We also study the geometric valuation for plane curves.

Related

• Geometry on arc spaces of algebraic varieties
• Zero dimensional arc valuations on smooth varieties
• On the arc filtration for the singularities of Arnold's lists
• The space of arcs of an algebraic variety
• Contact loci in arc spaces