250161 SE Algebraic geometry (2019S)

The course "Algebraic Geometry II" of the spring term 2019 will cover, among other things, the following topics:

* Recap on affine schemes
* Smooth and singular points, transversality, normal crossings
* Tangent spaces and tangent maps, module of differentials
* General schemes, gluing, sheaves
* Projective schemes, completeness
* Dimension theory (Krull dimension, Hilbert function and Hilbert polynomial)
* Morphisms: flat, proper, smooth, étale, birational morphisms, fiber dimension
* Blowups and resolution of singularities
* Normalization, Nash modification
* Classical theorems (Chevalley, Zariski, Chow, Mumford, Cohen, ...)

A basic knowledge about algebraic varieties is profitable, but it is not necessary to have attended the first part of the course (for which, however, lecture notes exist).

The course is blocked, since no class will be held during four weeks of the term. Schedule:

VO: Tuesday and Wednesday, 9:45 - 11:15, HS 11
PS: Tuesday, 16:45 - 18:15, SR 10