# Embedding codimension of the space of arcs

@article{Chiu2020EmbeddingCO, title={Embedding codimension of the space of arcs}, author={Ching-Ya Chiu and Tommaso de Fernex and Roi Docampo}, journal={arXiv: Algebraic Geometry}, year={2020} }

We introduce a notion of embedding codimension of an arbitrary local ring, establish some general properties, and study in detail the case of arc spaces of schemes of finite type over a field. Viewing the embedding codimension as a measure of singularities, our main result can be interpreted as saying that the singularities of the arc space are maximal at the arcs that are fully embedded in the singular locus of the underlying scheme, and progressively improve as we move away from said locus… CONTINUE READING

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