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Contact loci in arc spaces

Published online by Cambridge University Press:  04 December 2007

Lawrence Ein ,
Robert Lazarsfeld  and
Mircea Mustaţa
Lawrence Ein
Affiliation:
Department of Mathematics, University of Illinois at Chicago, 851 South Morgan Street (M/C 249), Chicago, IL 60607-7045, USAein@math.uic.edu
Robert Lazarsfeld
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USArlaz@umich.edu
Mircea Mustaţa
Affiliation:
Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USAmirceamustata@yahoo.com
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Abstract

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We give a geometric description of the loci in the arc space defined by order of contact with a given subscheme, using the resolution of singularities. This induces an identification of the valuations defined by cylinders in the arc space with divisorial valuations. In particular, we recover the description of invariants coming from the resolution of singularities in terms of arcs and jets.

Keywords

arc spacevaluationlog-canonical thresholdmultiplier ideals14B05 (primary)14E15 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 5 , September 2004 , pp. 1229 - 1244
Copyright
Foundation Compositio Mathematica 2004