Contact loci in arc spaces
Loading...
Date
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We study loci of arcs on a smooth variety defined by order of contact with a fixed subscheme. Specifically, we establish a Nash-type correspondence showing that the irreducible components of these loci arise from (intersections of) exceptional divisors in a resolution of singularities. We show also that these loci account for all the valuations determined by irreducible cylinders in the arc space. Along the way, we recover in an elementary fashion-without using motivic integration-results of the third author relating singularities to arc spaces. Moreover, we extend these results to give a jet-theoretic interpretation of multiplier ideals.
18 pages; v.2: minor changes; final version, to appear in Compositio Math
18 pages; v.2: minor changes; final version, to appear in Compositio Math