36 citations · 42 across the 3 of their papers we have counts for
5 papers
Homological Projective Duality
Alexander Kuznetsov
We introduce a notion of Homological Projective Duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If al…
Derived category of V_{12} Fano threefolds
Alexander Kuznetsov
A V_{12} Fano threefold is a smooth Fano threefold X of index 1 with Pic X = Z and (-K_X)^3=12. We show that the bounded derived category of coherent sheaves on any V_{12} threefol…
Derived categories of cubic and V14 threefolds
Alexander Kuznetsov
We show that the projectivization of the exceptional rank 2 vector bundle on an arbitrary smooth V14 Fano threefold after a certain natural flop turns into the projectivization of…
Wilson's grassmannian and a noncommutative Quadric
Vladimir Baranovsky, Victor Ginzburg, Alexander Kuznetsov
Let the group G of m-th roots of unity act on the complex line by multiplication, inducing an action on the algebra, Diff, of polynomial differential operators on the line. Followi…
Quiver varieties and Hilbert schemes
Alexander Kuznetsov
In this note we give an explicit geometric description of some of the Nakajima's quiver varieties. More precisely, we show that the -equivariant Hilbert scheme and th…