DE

Modul

Algebraic Geometry [M-MATH-101724]

Credits
8
Recurrence
Unregelmäßig
Duration
1 Semester
Language
Level
4
Version
1

Responsible

Organisation

  • KIT-Fakultät für Mathematik

Part of

Bricks

Identifier Name LP
T-MATH-103340 Algebraic Geometry 8

Competence Certificate

The module will be completed by an oral exam of about 30 minutes.

Competence Goal

Participants are able to 

  • name and discuss basic concepts concerning algebraic varieties
  • apply algebraic tools, in particular those from the theory of polynomial rings, to geometric questions
  • explain important results from classical algebraic geometry and their application in specific examples
  • start to read recent research papers from algebraic geometry and write a thesis in this area.

Prerequisites

None

Content

  • Hilbert's Nullstellensatz
  • affine and projective varieties
  • morphisms and rational maps
  • non-singular varieties
  • algebraic curves
  • Riemann-Roch-Theorem

Recommendation

The contents of basic courses on algebra and number theory, including basic commutative algebra, should be well-understood.

Workload

Total work load:

Attendance: 90 minutes

  • lectures, problem classes an examination

Self studies: 150 hours

  • follow-up and deepening of the course contents
  • work on problem sheets
  • literature study and internet research relating to the course contents
  • Preparation of the oral exam