7 papers
Filtrations on D-modules and multiplicities of roots of Bernstein-Sato polynomials
Andras Lorincz, Ruijie Yang
In this paper, we relate multiplicities of Bernstein--Sato-type polynomials with respect to a holomorphic function f to several singularity invariants. First, we introduce certain…
Multivariate V-filtrations and the Strong Monodromy Conjecture for hyperplane arrangements
Dougal Davis, Ruijie Yang
In this work, we develop a new theory of multivariate V-filtration on D-modules along a simple normal crossing divisor and relate it with Sabbah's multi-filtration. We establish se…
Filtrations of D-modules along semi-invariant functions
András C. Lőrincz, Ruijie Yang
Given a smooth algebraic variety X with an action of a connected reductive linear algebraic group G, and an equivariant D-module M, we study the G-decompositions of the associated…
On the Hodge and V-filtrations of mixed Hodge modules
Dougal Davis, Ruijie Yang
In this paper, we prove a Beilinson-type formula for the V-filtration of Kashiwara and Malgrange on a complex mixed Hodge module, using Hodge filtrations on the localization. Our f…
Archimedean zeta functions, singularities, and Hodge theory
Dougal Davis, András C. Lőrincz, Ruijie Yang
We use Hodge theory to relate poles of the Archimedean zeta function of a holomorphic function with several invariants of singularities. First, we prove that the largest…
Higher multiplier ideals
Christian Schnell, Ruijie Yang
We associate a family of ideal sheaves to any Q-effective divisor on a complex manifold, called higher multiplier ideals, using the theory of mixed Hodge modules and V-filtrations.…
Higher Du Bois and higher rational singularities of hypersurfaces
Laurenţiu Maxim, Ruijie Yang
In this note, we give several equivalent characterizations of higher Du Bois and higher rational singularities in the context of globally defined hypersurfaces. As a key input, we…