Related papers: Mixed Hodge complexes and L^2-cohomology for local…

We study the Hodge conjecture for certain families of varieties over arithmetic quotients of balls and Siegel domain of degree two. As a byproduct, we derive formulas for Hodge numbers in terms of automorphic forms.

Let X be a locally symmetric space associated to a reductive algebraic group G defined over Q. L-modules are a combinatorial analogue of constructible sheaves on the reductive Borel-Serre compactification of X; they were introduced in…

In this article, we pursue two main objectives. The first is to show that the fundamental results of Green-Lazarsfeld (1987, 1991) on generic vanishing theorems, and works of Budur-Wang (2015, 2020) on cohomology jumping loci, can be…

In this paper, we investigate the $L^2$-Dolbeault cohomology of the symmetric power of cotangent bundles of ball quotients with finite volume, as well as their toroidal compactification. Through the application of Hodge theory for complete…

Let $\textbf{H} = ((H, F^{\bullet}), L)$ be a polarized variation of Hodge structure on a smooth quasi-projective variety $U.$ By M. Saito's theory of mixed Hodge modules, the variation of Hodge structure $\textbf{H}$ can be viewed as a…

In this paper we study mixed Hodge structures on the cohomology of locally symmetric varieties and give an application to modular forms. After proving vanishing of some Hodge numbers, we focus on the weight filtration on the last Hodge…

Let $X$ be a Hilbert modular variety and $\mathbb{V}$ a non-trivial local system over $X$ with infinite monodromy. In this paper we study Saito's mixed Hodge structure (MHS) on the cohomology group $H^k(X,\mathbb{V})$ using the method of…

We study the Hodge filtration on the local cohomology sheaves of a smooth complex algebraic variety along a closed subscheme Z in terms of log resolutions, and derive applications regarding the local cohomological dimension, the Du Bois…

We study the 0-th local cohomology module of the jacobian ring of a singular reduced complex projective hypersurface X, by relating it to the sheaf of logarithmic vector field along X. We investigate the analogies between the local…

Andreotti-Vesentini, Ohsawa, Gromov, Koll\'ar, among others, have observed that Hodge theory could be extended to (non compact) K\"ahler complete manifolds, within the L^2 framework. Also, many vanishing theorems on projective or K\"ahler…

We give methods to compute l^2-cohomology groups of a covering manifolds obtained by removing pullback of a (normal crossing) divisor to a covering of a compact K\"ahler manifold. We prove that in suitable quotient categories, these groups…

In this paper we study the local cohomology of all finitely generated bigraded modules over a standard bigraded polynomial ring which have only one nonvanishing local cohomology with respect to one of the irrelevant bigraded ideals.

M. Goresky, G. Harder, and R. MacPherson defined weighted cohomologies of arithmetic groups \Gamma in a real group G, with coefficients in certain local systems, associated to arbitrary upper and lower weight profiles. The author shows,…

We compute the local intersection cohomology of the irreducible components of varieties of complexes, by using Lusztig's geometric approach to quantum groups and explicit constructions of elements of Lusztig's canonical bases.

The purpose of this paper is applying minimality of hyperplane arrangements to local system cohomology groups. It is well known that twisted cohomology groups with coefficients in a generic rank one local system vanish except in the top…

We consider the loci of d-elliptic curves in $M_2$, and corresponding loci of d-elliptic surfaces in $A_2$. We show how a description of these loci as quotients of a product of modular curves can be used to calculate cohomology of natural…

We compute the sheaf cohomology with constant $\mathbb{Z}_2$ coefficients of a concrete class of locally profinite sets of independent interest. We introduce $k$-sheer partitions to aid in constructions. It is also shown that questions of…

We employ the inductive structure of determinantal varieties to calculate the mixed Hodge module structure of local cohomology modules with determinantal support. We show that the weight of a simple composition factor is uniquely determined…

We study cohomology with coefficients in a rank one local system on the complement of an arrangement of hyperplanes $\A$. The cohomology plays an important role for the theory of generalized hypergeometric functions. We combine several…

This article constructs Von Neumann invariants for constructible complexes and coherent D-modules on compact complex manifolds, generalizing the work of the author on coherent L 2-cohomology. We formulate a conjectural generalization of…