Research Group:

## Algebraic Geometry

The first 48 hours of the course form an introduction to the language of schemes and coherent sheaves, and cover the material in Hartshorne, Algebraic Geometry, Section II.1-II.8: sheaves; schemes; open and closed subschemes, affine, finite, projective morphisms; properness and separatedness; quasicoherent and coherent sheaves, pushforward and pullback; divisors and invertible sheaves; Proj construction and blow-ups, sheaf of differentials. The remaining 12 hours will cover a quick introduction to infinitesimal deformation theory: Artinian local algebras, deformation fu