2 citations · 5 across the 19 of their papers we have counts for
23 papers
A Hodge module construction of relative Du Bois complexes
Bradley Dirks
We construct relative Du Bois and relative intersection Du Bois complexes for smooth-factorizable morphisms to a smooth complex base using relative de Rham complexes of mixed Hodge…
Filtrations on Local Cohomology and Injectivity Theorems
Qianyu Chen, Bradley Dirks, Sebastian Olano
We prove that the Hodge filtration on local cohomology is contained in the symbolic Ext filtration, and hence in the usual Ext filtration, answering a question of Mustata and Popa.…
-nilpotence and Hodge filtrations beyond isolated singularities
Bradley Dirks, Jakub Witaszek
We give Hodge-theoretic characterizations of characteristic-zero varieties of open -nilpotent and open weakly -nilpotent type, extending a result of Srinivas and Takagi beyon…
A Hodge Theoretic Generalization of -Homology Manifolds II: Local Complete Intersections
Bradley Dirks, Sebastian Olano, Debaditya Raychaudhury
Recently, the authors introduced and studied a singularity invariant of a complex algebraic variety , written $\HRH(Z)$ (for ``Hodge rational homology'' manifold level). In this…
Microlocal Bernstein--Sato polynomials on singular ambient varieties
Bradley Dirks, Michael Perlman
We introduce the microlocal Bernstein--Sato polynomial of a function on a possibly singular ambient variety, extending the theory of Saito. We show that, contrary to the smooth amb…
Characterization and finite descent of local cohomological invariants
Bradley Dirks, Sebastian Olano, Debaditya Raychaudhury
We provide simple ``left-inverse characterizations'' of the recently introduced singularity invariants , , and of an equidimensional variety . Combini…
Hodge theory of secant varieties
Qianyu Chen, Bradley Dirks, Sebastian Olano +1
We study the local cohomology modules for the secant variety of lines of a smooth projective variety and for higher secant varieties of smooth projective curves. We show that t…
Partial Cohomologically Complete Intersections via Hodge Theory
Qianyu Chen, Bradley Dirks, Sebastian Olano
We introduce an invariant associated to any complex algebraic variety , which for varieties with isolated singularities measures the failure of dual Kodaira-Akizuki-Nakan…
Multiplier modules, -filtrations and Bernstein-Sato polynomials on singular ambient varieties
Bradley Dirks
We show that the relation between multiplier ideals and -filtration on the structure sheaf due to Budur-Mustaţă-Saito generalizes to singular irreducible varieties, by replacing…
Hirzebruch-Milnor classes of local complete intersections, minimal exponent, and applications to higher singularities
Bradley Dirks, Laurenţiu Maxim, Sebastián Olano
In this paper we use the deformation to the normal cone and the corresponding Verdier-Saito specialization to define and study (spectral) Hirzebruch-Milnor type homology characteri…
A Hodge Theoretic generalization of -Homology Manifolds I: General Case
Bradley Dirks, Sebastian Olano, Debaditya Raychaudhury
We study a natural Hodge-theoretic generalization of rational (or -)homology manifolds through an invariant $\HRH(Z)$ attached to a complex algebraic variety . The d…
Restrictions of mixed Hodge modules using generalized V-filtrations
Qianyu Chen, Bradley Dirks, Sebastian Olano
We study generalized -filtrations, defined by Sabbah, on -modules underlying mixed Hodge modules on . Using cyclic covers, we compare these filt…
Fourier transform and Radon transform for mixed Hodge modules
Bradley Dirks
We give a generalization to bi-filtered -modules underlying mixed Hodge modules of the relation between microlocalization along and va…
The minimal exponent of cones over smooth complete intersection projective varieties
Qianyu Chen, Bradley Dirks, Mircea Mustaţă
We compute the minimal exponent of the affine cone over a complete intersection of smooth projective hypersurfaces intersecting transversely. The upper bound for the minimal expone…
An introduction to -filtrations
Qianyu Chen, Bradley Dirks, Mircea Mustaţă
We give an introduction to the theory of -filtrations of Malgrange and Kashiwara. After discussing the basic properties of this construction (in the case of a smooth hypersurfac…
Some applications of microlocalization for local complete intersection subvarieties
Bradley Dirks
Saito's microlocalization construction has been used to great effect in understanding hypersurface singularities. In this paper, we introduce what we believe to be a suitable analo…
Verdier specialization and restrictions of Hodge modules
Qianyu Chen, Bradley Dirks, Morihiko Saito
We give an explicit formula to express the cohomological pullback functors of Hodge modules under closed immersions of smooth varieties using Verdier specializations and -filtra…
The minimal exponent and -rationality for local complete intersections
Qianyu Chen, Bradley Dirks, Mircea Mustaţă
We show that if is a local complete intersection subvariety of a smooth complex variety , of pure codimension , then has -rational singularities if and only if $\w…
V-filtrations and minimal exponents for locally complete intersection singularities
Qianyu Chen, Bradley Dirks, Mircea Mustaţă +1
We define and study a notion of minimal exponent for a locally complete intersection subscheme of a smooth complex algebraic variety , extending the invariant defined by Sai…
On -filtration, Hodge filtration and Fourier transform
Qianyu Chen, Bradley Dirks
For a closed immersion of smooth varieties, we study how the -filtration along and the Hodge filtration on a mixed Hodge module on interact with each o…
Minimal exponents of hyperplane sections: a conjecture of Teissier
Bradley Dirks, Mircea Mustata
We prove a conjecture of Teissier asserting that if has an isolated singularity at and is a smooth hypersurface through , then $\widetildeα_P(f)\geq \widetildeα_P(f\…
The Hilbert series of Hodge ideals of hyperplane arrangements
Bradley Dirks, Mircea Mustata
Given a reduced effective divisor D on a smooth variety X, we describe the generating function for the classes of the Hodge ideals of D in the Grothendieck group of coherent sheave…
Upper bounds for roots of B-functions, following Kashiwara and Lichtin
Bradley Dirks, Mircea Mustata
By building on a method introduced by Kashiwara and refined by Lichtin, we give upper bounds for the roots of certain b-functions associated to a regular function f in terms of a l…