177 citations · 1.9k across the 60 of their papers we have counts for
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math.AG2019★ 3 cited
Rationality of Fano threefolds over non-closed fields
Alexander Kuznetsov, Yuri Prokhorov
We give necessary and sufficient conditions for unirationality and rationality of Fano threefolds of geometric Picard rank-1 over an arbitrary field of zero characteristic.
math.AG2019★ 6 cited
Categorical cones and quadratic homological projective duality
Alexander Kuznetsov, Alexander Perry
We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe…
math.AG2019
Homological projective duality for quadrics
Alexander Kuznetsov, Alexander Perry
We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projectiv…