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arXiv · 1506.06424

The volume of a set of arcs on a variety

Tommaso de Fernex·Mircea Mustata
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Abstract

In this paper, we give a definition of volume for subsets in the space of arcs of an algebraic variety, and study its properties. Our main result relates the volume of a set of arcs on a Cohen-Macaulay variety to its jet-codimension, a notion which generalizes the codimension of a cylinder in the arc space of a smooth variety.

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Tommaso de Fernex, Mircea Mustata. 2015-06-21. The volume of a set of arcs on a variety. https://arxiv.org/abs/1506.06424

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