Generically finite morphisms and formal neighborhoods of arcs

2007/08/29 by Lawrence Ein, Ein, Lawrence, Mircea Mustaţă +1
Computer Science · Engineering · #14B10 (Primary) 14B20 (Secondary) #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Computational Geometry and Mesh Generation #Constraint Satisfaction and Optimization #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0708.3880

openalex publication_date 2007/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that given a dominant morphism between two smooth varieties of the same dimension, the induced morphism between the formal neighborhoods of two arcs on these varieties is a closed embedding, of codimension given by the order of vanishing along the ramification subscheme.

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• Formal neighborhoods in arc spaces
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• Generically Finite Morphisms
• The Drinfeld-Grinberg-Kazhdan theorem and embedding codimension of the arc space
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