2003/03/31 by Lawrence Ein, Robert Lazarsfeld, Mircea Mustata · 1 citation
Mathematics · #math.AG #msc:14B05 #msc:14E15 #msc:14E30
published as Compositio Math. 140 (2004), 1229-1244. · 18 pages; v.2: minor changes; final version, to appear in Compositio Math
arxiv created 2004/04/12 · arxiv updated 2009/11/30
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.