Yu.Burman
Symmetric powers

Elemetary examples: symmetric powers of curves

Smoothness

Sphere, punctured sphere, elliptic curve

Local algebra

Weierstrass preparatory theorem

The degree of a mapping is equal to the dimension of its local algebra.
Example: quotient map f: X^{n} > X^{(n)}.

Mcdonald's formula for cohomology of a symmetric power.

Resolution of singularities of the symmetric power of a surface.

Hilbert scheme and Chow morphism. The ADHM model for a Hilbert scheme of
points in C^{2}.

Smoothness of the Hilbert scheme (Fogarty theorem).

Cohomology of the Hilbert scheme of points in a surface.

Goettsche formula for Betti numbers (without proof).

Action of the Heisenberg algebra on the cohomology (Nakajima operators).

The Fock space of semiinfinite forms.