Departmental Colloquium
Izzet Coskun
UIC
The Hilbert Scheme of Points
Abstract: The Hilbert scheme of $n$-points $X^{[n]}$ is a
`compactification' of the set of unordered $n$-tuples of distinct
points on a projective manifold $X$. When the dimension of $X$ is
two, $X^{[n]}$ is a smooth, projective manifold with many remarkable
properties. Consequently, it plays a central role in many areas of
mathematics ranging from representation theory to algebraic geometry
and from algebraic combinatorics to symplectic geometry. For
example, $X^{[n]}$ provide examples of holomorphic symplectic
manifolds when $X$ is a holomorphic, symplectic surface. The homology
of $X^{[n]}$ has the structure of an irreducible representation of
the Heisenberg superalgebra. Similarly, $X^{[n]}$ play a central role
in resolutions of canonical surface singularities. In this talk, I
will give a brief introduction to the Hilbert scheme of points and
its many amazing properties.
Friday September 14, 2012 at 3:00 PM in SEO 636