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Contact loci in arc spaces

Published online by Cambridge University Press:  04 December 2007

Lawrence Ein
Affiliation:
Department of Mathematics, University of Illinois at Chicago, 851 South Morgan Street (M/C 249), Chicago, IL 60607-7045, [email protected]
Robert Lazarsfeld
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, [email protected]
Mircea Mustaţa
Affiliation:
Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, [email protected]
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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.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2004