8 citations · 10 across the 5 of their papers we have counts for
10 papers
Coniveau and the Grothendieck group of varieties
Donu Arapura, Su-Jeong Kang
It is shown that if the generalized Hodge conjecture, or some weaker form of it, holds for a Calabi-Yau variety then it holds for any Calabi-Yau variety birationally equivalent to…
The Hodge conjecture for rationally connected fivefolds
Donu Arapura
The Hodge conjecture is shown to hold for rationally connected fivefolds, or more generally for fivefolds for which the base of the maximal rationally connected fibration is at mos…
Functoriality of the coniveau filtration
Donu Arapura, Su-Jeong Kang
There is a natural descending filtration on the singular cohomology of a complex smooth projective variety called the coniveau filtration. The generalized Hodge conjecture would im…
Partial Regularity and Amplitude
Donu Arapura
This is a sequel to the paper "Frobenius amplitude and strong vanishing theorems for vector bundles" (math.AG/0202129). We introduce a more elementary variant of the notion of F-am…
Kähler Solvmanifolds
Donu Arapura
Compact Kähler solvmanifolds are classified up to biholomorphism. A proof of a conjecture Benson and Gordon, that completely solvable compact Kähler solvmanifolds are tori is deduc…
Frobenius amplitude and strong vanishing theorems for vector bundles
Donu Arapura, Dennis S. Keeler
The primary goal of this paper is to systematically exploit the method of Deligne-Illusie to obtain Kodaira type vanishing theorems for vector bundles and more generally coherent s…