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Jet schemes, arc spaces and the Nash problem. (English) Zbl 1162.14006

This is a nice short expository article about jet schemes and arc spaces. Its purpose is to be introductory rather than comprehensive. The author also gives an introduction to the Nash problem which asks when there is a bijection between certain exceptional divisors in a log resolution and certain irreducible components of the space of arcs at singular points.

MSC:

14D15 Formal methods and deformations in algebraic geometry
14D22 Fine and coarse moduli spaces
14J17 Singularities of surfaces or higher-dimensional varieties
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