Hilbert and Picard schemes, deformations and representability

Twelve lessons on parameter spaces for subschemes, quotient sheaves and line bundles, with their deformation theory. The supporting reading treats multiplicative-group cohomology and change of topology.

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1. Representable functors and the functor of points
2. Grassmannians
3. Regularity and bounded families
4. Flattening stratifications
5. Hilbert and Quot schemes
6. Formal moduli and Schlessinger's theorem
7. Deformations of rings and schemes and the naive cotangent complex
8. Tangent spaces and obstructions for Hilbert and Quot schemes
9. The Picard functor and the Picard scheme of a curve
10. Relative divisors and the existence of the Picard scheme
11. The structure of the Picard scheme
12. The cotangent complex

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