10 papers
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…
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…
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
Using Saito's theory of mixed Hodge modules, we study a generalization of Hellus-Schenzel's "cohomologically complete intersection" property. This property is equivalent to pervers…