Contact loci in arc spaces
By L. Ein, R. Lazarsfeld, M. Mustaţă. Compositio Mathematica, 2003
107 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/70567bc25477011f3f6fca5c4ea30bb8d3d09fdf
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The arc space of a toric variety (2003, methodology): “X. Note that this definition is wider than the definition of “divisorial valuation” in [ 6 ].”
- Bounds for log canonical thresholds with applications to birational rigidity (2002, methodology): “∗+ and bi ∈ Q, such that µ ≥ maxi{bi}. If the pair (An, 1 µ(V + P i biHi)) is not log terminal, then l(R/a) ≥ nn n! · Yn i=1 (µ−bi), and the inequality is strict if n ≥ 2. Proof. We use the result in [ELM] which gives the condition for a monomial pair, with possibly negative coefficients, to be log te”
- Birationally rigid hypersurfaces (2006, methodology): “usual methods relying on vanishing theorems cannot be employed. The proof of Theorem B uses the characterization of divisorial valuations and log-discrepancies via contact loci in arc spaces given in [ELM]. In order to apply the above result to prove Theorem A, we use generic projections in a simila”
- Arc spaces, motivic integration and stringy invariants (2004, background): “† Ein, Lazarsfeld, Mustat»•a and Yasuda have various other papers about spaces of jets, relating them for instance to singularities of pairs, in particular to the log canonical threshold, and to multiplier ideals [ ELM ][Mu2][Ya2].”
- Arcs, valuations and the Nash map (2004, background): “The paper [ 4 ] defines a valuation valC of K(X) corresponding to C and proves that valC is a divisorial valuation.”