We define multi-indexed Deligne extensions and multi-indexed log-variations of Hodge structures in the category of (filtered) logarithmic D-modules, via the idea of Bernstein– Sato polynomials and Kashiwara–Malgrange filtrations, generalizing the Deligne canonical extensions of flat vector bundles. We also obtain many comparison results with perverse sheaves via the logarithmic de Rham functor. Based on multi-indexed Deligne extensions, we define multiplier subsheaves for pure Hodge modules (geometrically for higher direct images of dualizing sheaves for projective families) on algebraic varieties, which specialize to multiplier ideals when the pure Hodge module is trivial. From Kodaira–Sato vanishing for Hodge modules, we obtain a Nadel- type vanishing theorem for multiplier subsheaves, which in the geometric case generalizes both Kolla ́r vanishing for higher direct images of dualizing sheaves and Nadel vanishing for multiplier ideals. As an application, we use it to deduce a Fujita-type effective global generation theorem extending a result of Kawamata for higher direct images of dualizing sheaves.

Last modified

• 03/26/2018

Creator

• Lei Wu

DOI

• https://doi.org/10.21985/N24X2T

Subject

• Mathematics

Keyword

• Birational Geometry
• Hodge theory
• Algebraic Geometry
• D-modules

Date created

• 2017-01-01

Resource type

• Dissertation

Rights statement

• In Copyright