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Kuchle fivefolds of type c5

Speaker: 
Alexander Kuznetsov
Institution: 
Steklov Mathematical Institute, Moscow
Schedule: 
Friday, July 29, 2016 - 14:30
Location: 
A-136
Abstract: 

A Kuchle fivefold of type c5 is a subvariety of the Grassmannian Gr(3,7) parameterizingsubspaces isotropic for a given 2-form and annihilated by a given 4-form on a 7-dimensional space.It is expected that general hyperplane sections of these fivefolds (Kuchle fourfolds of type c5)are analogous to cubic fourfolds in many ways --- they have a rich birational structure, theirderived categories contain noncommutative K3 categories, and some moduli spaces of sheaves onthem are hyperkahler varieties. In the talk I will describe a geometric description of thesefivefolds, relating them to hyperplane sections of Lagrangian Grassmannian LGr(3,6) and as a consequence will show that the integral Chow motive of these varieties is Lefschetz.

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