Curve selection lemma in arc spaces

2022/12/31 by Nguyen Hong Duc, Duc, Nguyen Hong
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2301.00128

openalex publication_date 2022/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first generalize a curve selection lemma for Noetherian schemes and apply it to prove a version of Curve Selection Lemma in arc spaces, answering affirmatively a question by Reguera. Furthermore, thanks to a structure theorem of Grinberg, Kazhdan and Drinfeld, we obtain other versions of Curve Selection Lemma in arc spaces.

Related

• Curve selection lemma in infinite dimensional algebraic geometry and arc spaces
• Rationally generated arcs
• Greenberg approximation and the geometry of arc spaces
• Geometry on arc spaces of algebraic varieties
• The space of arcs of an algebraic variety