Contact loci in arc spaces

Lawrence Ein; Robert Lazarsfeld; Mircea Mustaţǎ

doi:10.1112/S0010437X04000429

Contact loci in arc spaces

Lawrence Ein
, Robert Lazarsfeld
, Mircea Mustaţǎ

Mathematics

University of Illinois at Chicago
Harvard University

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

We give a geometric description of the loci in the arc space defined by order of contact with a given snbscheme, 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.

Original language	English
Pages (from-to)	1229-1244
Number of pages	16
Journal	Compositio Mathematica
Volume	140
Issue number	5
DOIs	https://doi.org/10.1112/S0010437X04000429
State	Published - 2004

Keywords

Arc space
Log-canonical threshold
Multiplier ideals
Valuation

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10.1112/S0010437X04000429

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abstract = "We give a geometric description of the loci in the arc space defined by order of contact with a given snbscheme, 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.",

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AU - Ein, Lawrence

AU - Lazarsfeld, Robert

AU - Mustaţǎ, Mircea

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N2 - We give a geometric description of the loci in the arc space defined by order of contact with a given snbscheme, 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.

AB - We give a geometric description of the loci in the arc space defined by order of contact with a given snbscheme, 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.

KW - Arc space

KW - Log-canonical threshold

KW - Multiplier ideals

KW - Valuation

UR - https://www.scopus.com/pages/publications/29344435864

U2 - 10.1112/S0010437X04000429

DO - 10.1112/S0010437X04000429

M3 - Article

AN - SCOPUS:29344435864

SN - 0010-437X

VL - 140

SP - 1229

EP - 1244

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 5

ER -

Contact loci in arc spaces

Abstract

Keywords

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