Multiplier ideals, V-filtration, and spectrum

Details Multiplier ideals, V-filtration, and spectrum Multiplier ideals, V-filtration, and spectrum

2003-05-08

arxiv.org/abs/math/0305118v5

Mathematics

Algebraic Geometry

13 pages, the statement of the main theorem is improved

Scientific paper

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.

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