2 citations · 5 across the 19 of their papers we have counts for
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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…