On Hodge spectrum and multiplier ideals
By Nero Budur. 2002
62 citations recorded by the source corpus.
Abstract.We describe a relation between two invariants which measure the complexity of a hypersurface singularity. One is the Hodge spectrum which is related to the monodromy and the Hodge filtration on the cohomology of the Milnor fiber. The other is the multiplier ideal, having to do with log resolutions.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/dce132e28e826add40121e621aa9cd44cd65c725
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In Geometry and Topology
In Mathematical Physics
- Morihiko Saito
- L. Ein
- Karen E. Smith
- R. Lazarsfeld
- M. Mustaţă
- Tommaso de Fernex
- S. Ishii
- F. Forstnerič
Citations in the corpus
- Multiplier ideals, $b$-function, and spectrum of a hypersurface singularity (2004, background): “It is shown by Ein et al. (see [ELSV04]) that any jumping coefficients which are less than one are roots of the Bernstein–Sato polynomial bf (s) (i.e. the b-function) up to a sign.”
- Jumping coefficients of multiplier ideals (2003, background): “Then the Pk form a graded family with respect to Minkowski addition, i.e.”
- Jumping coefficients and spectrum of a hyperplane arrangement (2009, unknown): “In this case Mustaţǎ’s formula implies the following (see [22], Cor. 2.1): If α = j/d ∈ ( 2 3 , 1) with j ∈ Z, then (0.1) α ∈ JC(D) ⇐⇒ ∃ g ∈ C[x, y, z]j−3 \ {0} with g−1(0) ⊃ P(Dnnc).”
- Multiplier ideals, V-filtration, and spectrum (2003, unknown): “Then by (2.2–3) and (4.3) we get Kα = ωX′/X ⊗ F1−nGr α V Bf ′ ⊗OE(α) = ωX′/X ⊗ F1−n(i∗i ∗GrαV Bf ′), K ′α = ωX′/X ⊗ F1−nGr α V Bf ′ ⊗OE(α)(−E ′′(α)) = ωX′/X ⊗ F1−n(i∗i !”
- Bernstein–Sato polynomials of hyperplane arrangements (2006, unknown): “Let ωα = αi ωi + αj ωj + αl ωl with αi, αj, αl ∈ C ∗.”