Yu.Burman
Symmetric powers
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Elemetary examples: symmetric powers of curves
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Smoothness
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Sphere, punctured sphere, elliptic curve
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Local algebra
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Weierstrass preparatory theorem
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The degree of a mapping is equal to the dimension of its local algebra.
Example: quotient map f: Xn -> X(n).
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Mcdonald's formula for cohomology of a symmetric power.
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Resolution of singularities of the symmetric power of a surface.
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Hilbert scheme and Chow morphism. The ADHM model for a Hilbert scheme of
points in C2.
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Smoothness of the Hilbert scheme (Fogarty theorem).
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Cohomology of the Hilbert scheme of points in a surface.
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Goettsche formula for Betti numbers (without proof).
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Action of the Heisenberg algebra on the cohomology (Nakajima operators).
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The Fock space of semiinfinite forms.