5 papers
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…
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…
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…