12 citations · 19 across the 5 of their papers we have counts for
7 papers
Clifford spaces of empty intersections of quadrics
Alexander Kuznetsov
Given a linear space of quadrics in a projective space whose intersection is empty, we consider the corresponding Clifford space --…
Mukai models of Fano varieties
Arend Bayer, Alexander Kuznetsov, Emanuele Macrì
We give a self-contained and simplified proof of Mukai's classification of prime Fano threefolds of index 1 and genus with at most Gorenstein factorial terminal singulari…
Mukai bundles on Fano threefolds
Arend Bayer, Alexander Kuznetsov, Emanuele Macrì
We give a proof of Mukai's Theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literat…
One-nodal Fano threefolds with Picard number one
Alexander Kuznetsov, Yuri Prokhorov
We classify all 1-nodal degenerations of smooth Fano threefolds with Picard number 1 (both nonfactorial and factorial) and describe their geometry. In particular, we describe a rel…
Exceptional collections in surface-like categories
Alexander Kuznetsov
We provide a categorical framework for recent results of Markus Perling on combinatorics of exceptional collections on numerically rational surfaces. Using it we simplify and gener…
On Küchle manifolds with Picard number greater than 1
Alexander Kuznetsov
We describe the geometry of Küchle varieties (i.e. Fano 4-folds of index 1 contained in the Grassmannians as zero loci of equivariant vector bundles) with Picard number greater tha…
Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's
A. Kuznetsov, L. Manivel, D. Markushevich
It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed p-form with p=2n-4 on the Fano scheme of…