Algebraic Surfaces

What it is about

You deal with algebraic curves and surfaces, their classifications and the birational geometry of surfaces. In the end you know the classification (Kodaira–Enriques), minimal models, blow-ups, and important surfaces classes such as rational, elliptic, del Pezzo, K3 and Enriques surfaces; you can apply theoretical statements and compute invariants in concrete examples.

What you will be able to do

• Classification of algebraic surfaces (Kodaira–Enriques)
• Birational geometry: blow-ups, minimal models, Castelnuovo's theorem
• Knowledge of important surface classes: rational, elliptic, del Pezzo, K3, Enriques, general type
• Apply theory to explicit examples (hypersurfaces, branched covers)
• Computation of basic invariants (Betti numbers, plurigenera) in concrete cases

What the module consists of

• VorlesungDelivery of definitions and theoretical results on the theory of algebraic surfaces
• Übungs-/BeispielstundenApplication of techniques to explicit examples; deepening and solving exercises
• ÜbungsblätterPreparation for the exercise sessions; working on and discussion of solutions

Teaching method

• PräsenzvorlesungIntroduction to terms and proofs of the theory
• Übungs-/BeispielstundenApply and deepen lecture content using concrete tasks and examples
• ÜbungsblätterIndependent preparation of examples and techniques before the exercise sessions
• TafelunterrichtDetailed derivation and presentation of proofs and calculation examples