Compact HyperKähler category
Roland Abuaf (Imperial)  Seminar Algebraic Geometry (SAG)
What 


When 
Nov 05, 2015 from 10:30 am to 11:30 am 
Where  Bonn, Hörsaal MPI, Vivatsgasse 7 
Contact Name  Sachinidis 
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Along with complex tori and CalabiYau manifolds, compact hyperK\"ahler
manifolds are building blocks for the decomposition of Ricciflat
manifolds. All complex tori are classified, while we know how to
construct a "large number" of different deformation classes of CY
manifolds in each complex dimension (bigger than 3).
The situation for compact hyperK\"ahler manifolds is quite different.
We have absolutely no clue on how to classify them and we only know 2
infinite series and 2 sporadic examples of such manifolds. The last new
example of compact hyperK\"ahler manifold has been constructed 15 years
ago (O'Grady).
In this talk, I will introduce the notion of compact hyperK\"ahler
categories, study some of their invariance properties and some
construction techniques. In particular, I will show that one can
construct a "large number" of different deformation classes of compact
hyperK\"ahler categories in each even dimension.
If time permits, I will discuss a specific modular example, whose
Hochschild cohomology ring reveals some very interesting properties.