Multiplier ideals, V-filtration, and spectrum

By Nero Budur, Morihiko Saito. 2003

106 citations recorded by the source corpus.

For an effective divisor on a smooth algebraic variety or a complex manifold, we show that the associated multiplier ideals coincide essentially with the filtration induced by the filtration V constructed by B. Malgrange and M. Kashiwara. This implies another proof of a theorem of L. Ein, R. Lazarsfeld, K.E. Smith and D. Varolin that any jumping coefficient in the interval (0,1] is a root of the Bernstein-Sato polynomial up to sign. We also give a refinement (using mixed Hodge modules) of the formula for the coefficients of the spectrum for exponents not greater than one or greater than the dimension of the variety minus one.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c66c3b10bfbc9852148014a65d6bc92293fcf575

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In Geometry and Topology

1. Morihiko Saito
2. M. Mustaţă
3. Nero Budur
4. Chi Li
5. Mihnea Cristian Popa
6. S. Ishii
7. H. Blum
8. Mattias Jonsson

In Mathematical Physics

1. Morihiko Saito
2. M. Mustaţă
3. Nero Budur
4. S. Ishii
5. Tommaso de Fernex
6. L. Ein
7. Karl Schwede
8. H. Blum

Citations in the corpus

• Multiplier ideals, $b$-function, and spectrum of a hypersurface singularity (2004, methodology): “for � = exp(−2�i�) where Fx denotes the Milnor fiber around x and n = dimX, see [ 5 ].”
• HODGE IDEALS FOR $\mathbb{Q}$-DIVISORS, $V$-FILTRATION, AND MINIMAL EXPONENT (2018, unknown): “On the other hand, when D is integral Budur and Saito [ BS05 ] have shown the identification where V O X denotes the V -filtration induced on O X .”
• Bernstein–Sato polynomials of arbitrary varieties (2004, background): “Our first main theorem concerns the multiplier ideals and the V -filtration.”
• Bernstein–Sato polynomials of hyperplane arrangements (2006, unknown): “Let ωα = αi ωi + αj ωj + αl ωl with αi, αj, αl ∈ C ∗.”
• 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).”