6 papers · 1 filter
Homomorphisms between Kaehler groups
Donu Arapura
This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A…
The combinatorial part of the cohomology of a singular variety
Donu Arapura, Parsa Bakhtary, Jarosław Włodarczyk
We study the first step of the weight filtration on the cohomology of a proper complex algebraic variety, which we call the combinatorial part. We obtain a natural upper bound on i…
The Hodge theoretic fundamental group and its cohomology
Donu Arapura
In this paper, we explore a notion of nonabelian Hodge structure on the fundamental group of an algebraic variety. This is approach is compared to some alternative approaches due t…
Beilinson-Hodge cycles on semiabelian varieties
Donu Arapura, Manish Kumar
Beilinson conjectured that all rational cycles of type (q,q) on the qth cohomology of a smooth complex algebraic variety should come from motivic cohomology. The purpose of this no…
Mixed Hodge structures associated to geometric variations
Donu Arapura
The purpose of this note is prove that the mixed Hodge structure constructed by the author in math.AG/0301140 [The Leray spectral sequence is motivic, Invent. 2005] for geometric v…
The motive of the moduli stack of G-bundles over the universal curve
Donu Arapura, Ajneet Dhillon
An abelian category of relative pure motives is constructed along the lines of André (over a field of characteristic 0). An algebraic stack is shown to possess a motive in this sen…