Generically finite morphisms and formal neighborhoods of arcs
Lawrence Ein, Mircea Mustata
TL;DR
This paper proves that for a dominant morphism between smooth varieties of the same dimension, the induced morphism on formal neighborhoods of arcs is a closed embedding, with codimension related to ramification order.
Contribution
It establishes a precise relationship between morphisms of smooth varieties and their formal neighborhoods of arcs, highlighting the role of ramification.
Findings
Induced morphism between formal neighborhoods is a closed embedding.
Codimension of embedding is determined by the order of vanishing along the ramification.
Results connect geometric properties of morphisms with formal arc spaces.
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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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Constraint Satisfaction and Optimization · Computational Geometry and Mesh Generation