Hodge ideals for Q-divisors: birational approach

Abstract

We develop the theory of Hodge ideals for Q-divisors by means of log resolutions, extending our previous work on reduced hypersurfaces. We prove local (non-)triviality criteria and a global vanishing theorem, as well as other analogues of standard results from the theory of multiplier ideals, and we derive a new local vanishing theorem. The connection with the V-filtration is analyzed in a sequel.

Version 2: minor changes, including the title

References in corpus (2)

• Hodge ideals and microlocal V-filtration
• Hodge ideals for Q-divisors, V-filtration, and minimal exponent

Cited by in corpus (3)

• Hodge filtration and Hodge ideals for $\mathbb{Q}$-divisors with weighted homogeneous isolated singularities
• D-modules in birational geometry
• Hodge ideal and spectrum of weighted homogeneous isolated singularities