13 citations · 20 across the 6 of their papers we have counts for
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A natural Chow lemma for smooth threefolds and fourfolds
Parsa Bakhtary
Let be a smooth proper integral variety of dimension at most four over a field of characteristic zero. We construct a finite sequence of blowups along smooth centers with proje…
Sharp Bounds and Canonical Blow-ups for Toric Projectivization
Parsa Bakhtary
For every dimension , we construct a family of smooth complete fans with Picard number five and fixed combinatorial type. For integers , the minimum numb…
Weights on cohomology, invariants of singularities, and dual complexes
Donu Arapura, Parsa Bakhtary, Jarosław Włodarczyk
In this paper, we extract natural invariants of a singularity by using the Deligne weight filtration on the cohomology of an exceptional fibre of a resolution, and also on the inte…
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…
Splitting criteria for vector bundles on higher dimensional varieties
Parsa Bakhtary
We generalize Horrocks' criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth com…
On the cohomology of a simple normal crossings divisor
Parsa Bakhtary
We establish a formula which decomposes the cohomologies of various sheaves on a simple normal crossings divisor (SNC) in terms of the simplicial cohomologies of the dual compl…