177 citations · 1.9k across the 60 of their papers we have counts for
67 papers
Betti Numbers of Odd Biisotropic Symplectic Grassmannians
Anton Fonarev, Alexander Kuznetsov
We compute the singular cohomology groups of odd biisotropic symplectic Grassmannians by presenting an explicit dimension-preserving combinatorial b…
Derived categories of Fano threefolds and degenerations
Alexander Kuznetsov, Evgeny Shinder
Using the technique of categorical absorption of singularities we prove that the nontrivial components of the derived categories of del Pezzo threefolds of degree $d \in \{2,3,4,5\…
Explicit deformation of the horospherical variety of type
Alexander Kuznetsov
We give two simple geometric constructions of a smooth family of projective varieties with central fiber isomorphic to the horospherical variety of type and all othe…
Homologically finite-dimensional objects in triangulated categories
Alexander Kuznetsov, Evgeny Shinder
In this paper we investigate homologically finite-dimensional objects in the derived category of a given small dg-enhanced triangulated category. Using these we define reflexivity,…
On higher-dimensional del Pezzo varieties
Alexander Kuznetsov, Yuri Prokhorov
We study del Pezzo varieties, higher-dimensional analogues of del Pezzo surfaces. In particular, we introduce ADE classification of del Pezzo varieties, show that in type A the dim…
Derived categories of families of Fano threefolds
Alexander Kuznetsov
We construct -linear semiorthogonal decompositions of derived categories of smooth Fano threefold fibrations with relative Picard rank and rational geometric fibers an…