Joint Colloquium: Sukhendu Mehrotra -- Noncommutative K3 surfaces

Speaker: Dr. Sukhendu Mehrotra 

Time: Friday, May 17, 2:30--3:30PM 

Room: Chemistry Lecture Theatre 2, the University of Sydney 

Lunch plan: we meet near Level 2 entrance to Carslaw Building around 1PM.  

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Title: Noncommutative K3 surfaces 

Abstract: K3 surfaces are amongst the most studied surfaces in algebraic geometry.  What
makes the geometry of a K3 so interesting is that it carries a nondegenerate holomorphic
2-form: thus any K3 is a compact holomorphic symplectic manifold.  Examples of such
manifolds are quite rare, and their study and classification is an active area of
research.  

A particular example of a homolorphic symplectic manifold (discovered by Beauville) is
the Hilbert scheme $X^{[n]}$ parametrizing subsets (or subschemes) of $n$ points on a K3
surface $X$.  While any K3 varies in a 20-dimensional family, $X^{[n]}$ has a
21-dimensional space of deformations, and it is an open problem to give a geometric
description of these additional deformations.  This talk will attempt to explain how
this extra modulus may be seen to arise from ``noncommutative’’ deformations of $X$.
The presentation is aimed at a broad audience.  

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Joint Colloquium web site: 

http://www.maths.usyd.edu.au/u/SemConf/JointColloquium/index.html