Generically finite morphisms and formal neighborhoods of arcs

Details Generically finite morphisms and formal neighborhoods of arcs Generically finite morphisms and formal neighborhoods of arcs

2007-08-29

arxiv.org/abs/0708.3880v3

Mathematics

Algebraic Geometry

6 pages; final version, to appear in the Proceedings of the IV Iberoamerican Conference on Complex Geometry

Scientific paper

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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