Type: Seminar

Distribution: World

Auth: afish@p617.pc (assumed)

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. ----------------------------------------------- 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. ----------------------------------------------- Joint Colloquium web site: http://www.maths.usyd.edu.au/u/SemConf/JointColloquium/index.html