4 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…