The space of arcs of an algebraic variety
Tommaso de Fernex
TL;DR
This paper surveys the topology of the arc space of algebraic varieties and discusses the Nash problem related to the arc structure of singularities, highlighting key results and open questions.
Contribution
It provides a comprehensive overview of the topology of arc spaces and the Nash problem, synthesizing recent advances and unresolved issues.
Findings
Summary of key results on arc space topology
Discussion of the Nash problem on singularities
Identification of open questions in the field
Abstract
The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory