104.584 AKGEO Algebraic Geometry
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2021S, VU, 3.0h, 4.5EC


  • Semester hours: 3.0
  • Credits: 4.5
  • Type: VU Lecture and Exercise
  • Format: Distance Learning

Learning outcomes

After successful completion of the course, students are able to describe and apply fundamental concepts and methods of the theory of algebraic curves.

This theory has connections to the number theory, projective geometry, and complex analysis. In particular we will learn how to find all integer solutions of the equation x^2 - 21y^2 = 1, give algebraic proofs of incidence theorems of projective geometry, and use the complex structure in order to derive further geometric theorems.

Subject of course

Conics: affine and projective classification, rational parametrization, integer points on hyperbolas, pencils of conics.

Quadrics: classification, pencils, geometric theorems.

Cubics: group structure, parametrization with elliptic functions.

Teaching methods

Lecture, discussion of examples, homework.

Mode of examination

Written and oral

Additional information

The lecture will be given via Zoom, the communication done through TUWEL. Please register in TISS, the registration will be transferred to TUWEL.



Course dates

Thu13:00 - 15:3004.03.2021 - 25.03.2021 online via Zoom (LIVE)Vorlesung+Übung
Mon14:00 - 16:3012.04.2021 - 28.06.2021 (LIVE)Vorlesung+Übung (Zoom)
AKGEO Algebraic Geometry - Single appointments
Thu04.03.202113:00 - 15:30 online via ZoomVorlesung+Übung
Thu11.03.202113:00 - 15:30 online via ZoomVorlesung+Übung
Thu18.03.202113:00 - 15:30 online via ZoomVorlesung+Übung
Thu25.03.202113:00 - 15:30 online via ZoomVorlesung+Übung
Mon12.04.202114:00 - 16:30 Vorlesung+Übung (Zoom)
Mon19.04.202114:00 - 16:30 Vorlesung+Übung (Zoom)
Mon26.04.202114:00 - 16:30 Vorlesung+Übung (Zoom)
Mon03.05.202114:00 - 16:30 Vorlesung+Übung (Zoom)
Mon10.05.202114:00 - 16:30 Vorlesung+Übung (Zoom)
Mon17.05.202114:00 - 16:30 Vorlesung+Übung (Zoom)
Mon31.05.202114:00 - 16:30 Vorlesung+Übung (Zoom)
Mon07.06.202114:00 - 16:30 Vorlesung+Übung (Zoom)
Mon14.06.202114:00 - 16:30 Vorlesung+Übung (Zoom)
Mon21.06.202114:00 - 16:30 Vorlesung+Übung (Zoom)
Mon28.06.202114:00 - 16:30 Vorlesung+Übung (Zoom)

Examination modalities

Homework, oral exam. Possibly visualization in Mathematika or Geogebra. Projects for school.

Course registration

Begin End Deregistration end
17.02.2021 08:00



Stillwell "Numbers and geometry"

Gibson "Elementary geometry of algebraic curves"

Reid "Undergraduate algebraic geometry"

Previous knowledge

Matrix calculus, complex numbers.