2 citations · 2 across the 13 of their papers we have counts for
17 papers
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.…
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…
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…
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…
On the local cohomology of secant varieties
Sebastian Olano, Debaditya Raychaudhury
Given a sufficiently positive embedding of a smooth projective variety , we consider its secant variety that comes equipped with the embedding $Σ\subs…
Singularities of secant varieties from a Hodge theoretic perspective
Sebastian Olano, Debaditya Raychaudhury, Lei Song
We study the singularities of secant varieties of smooth projective varieties using methods from birational geometry when the embedding line bundle is sufficiently positive. More p…
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…
Weighted Hodge ideals of reduced divisors
Sebastian Olano
We study the Hodge and weight filtrations on the localization along a hypersurface, using methods from birational geometry and the -filtration induced by a local defining equati…
On a conjecture of Bitoun and Schedler
Mircea Mustata, Sebastian Olano
Suppose that is a smooth complex algebraic variety of dimension and defines a hypersurface in , with a unique singular point . Bitoun and Schedler conjec…
The Du Bois complex of a hypersurface and the minimal exponent
Mircea Mustata, Sebastian Olano, Mihnea Popa +1
We study the Du Bois complex of a hypersurface in a smooth complex algebraic variety in terms its minimal exponent . The latter is an in…
Weighted multiplier ideals of reduced divisors
Sebastian Olano
We use methods from birational geometry to study the Hodge and weight filtrations on the localization along a hypersurface. We focus on the lowest piece of the Hodge filtration of…
On the nonnegativity of stringy Hodge numbers
Sebastian Olano
We study the nonnegativity of stringy Hodge numbers of a projective variety with Gorenstein canonical singularities, which was conjectured by Batyrev. We prove that the -str…
Local vanishing and Hodge filtration for rational singularities
Mircea Mustata, Sebastian Olano, Mihnea Popa
Given an n-dimensional variety Z with rational singularities, we conjecture that for a resolution of singularities whose reduced exceptional divisor E has simple normal crossings,…