SMS scnews item created by Alexander Fish at Tue 7 May 2013 1430
Type: Seminar
Distribution: World
Calendar1: 17 May 2013 1430-1530
CalLoc1: Chemistry Lecture Theatre 2, the University of Sydney
Auth: afish@p617.pc (assumed)

# 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


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