Informationen zum Steilkurs Schemata/Fast track course schemes
Wintersemester 2022

Dozentin: Prof. Dr. Annette Huber-Klawitter
√úbungen: M.Sc. Luca Terenzi


The exercise class will be held in English. Some information on the planned content can be found in the kommentiertes Vorlesungsverzeichnis kommentierten Vorlesungsverzeichnis.


Here is are the class notes (pdf), version of 2.2.23.



Tuesday 08-10, SR 404, Ernst-Zermelo-Str. 1

Excercise and discussion classes

Thursday 10-12; Friday 10-12

Material covered and excercises

  • 20.12.22 Ample and very ample sheaves Ha II.5 and II.7

    Ha II 5.13, 5.16,5.18,7.5

  • 10.01.23 Differential forms Ha II 8, Matsumura: Commutative algebra

  • 17.01.23 Regularity and smoothness Ha I 5, II 8 and III 10

    Ha I 5.10, II 8.6, III 10.1 --

  • 24.01.23 Line bundles, Chech-cohomology and Cartier-divisors Ha II 6, III 4

    1. Check that the morphism in H^1 does not depend on the choice of a refinement morphism
    2. Check the exactness of the beginning of the long exact cohomology sequence (H^0 and H^1) for a short exaxt sequence of sheaves
    3. Make Cartier-divisors and line bundles explicit on the spectrum of a Dedekind domain
    4. Ha II 6.10
  • 31.1.23 Weil-Divisors and Cartier-Divisors Ha II 6

    Ha II 6.1, 6.6, using Examples 6.10.2, and in addition 6.5.2 and 6.11.3

  • 7.2.23 Weil conjectures




    1. R. Hartshorne. Algebraic Geometry. GTM52, Springer.