Arbeitsgruppe Komplexe Geometrie
Lehrveranstaltungen Prof. Dr. Daniel Huybrechts u. AG Komplexe Geometrie
im Wintersemester 2020/21:

Algebraic Geometry I (V4A1); Nr. 611500201
Prof. Huybrechts
Montag 16 c.t. - 18
Freitag 14 c.t. - 16
First lecture: October 30th.
Zoom details will be available on eCampus. Please register for the lecture on this course's eCampus page.
Language of instruction is English. The course is recommended to all Bachelor students who plan to write a bachelor thesis in algebraic geometry. (For those the course is accompanied by the seminar (S2A1).)

Covid measures: I plan to teach this class in a hybrid form, with a few students (not always the same) in the lecture hall, to allow for questions and general interaction. The lectures can be watched online by all other students not present. For the tutorials please see Uebungen Algebraic Geometry I (V4A1); Nr. 611700201

Content: This course is an introduction to the language of schemes (including sheaves and their cohomology), which are (ringed) spaces that locally look like the spectrum of a commutative ring. This is the language of modern algebraic geometry and was mainly developed by Grothendieck. The focus of the course will really be on schemes and not so much varieties (which will only be touched upon occasionally). Prerequisite for this course is a good knowledge of commutative algebra (to the extent of last term's course Algebra I).

One of the founders of the theory, David Mumford, wrote in 1975: [Algebraic geometry] seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics! In one respect this last point is accurate ...
Find out!

Some of the standard sources include:
  • R. Hartshorne: Algebraic Geometry GTM 52. Springer. (This is still the most commonly used source.)
  • D. Mumford: The Red book of varieties and schemes. Springer LN 1358.
  • R. Vakil: Foundations of algebraic geometry. Online lectures (
  • J. de Jong: The Stacks project (
  • D. Eisenbud and J. Harris, The Geometry of Schemes, GTM 197, Springer.
  • U. Goertz, T. Wedhorn: Algebraic Geometry I. Vieweg.
  • Q. Liu: Algebraic Geometry and Arithmetic Curves. Oxford GTM

  • Uebungen Algebraic Geometry I (V4A1); Nr. 611700201
    Dr. Gebhard Martin
    We. 12-14 (in-person); Th. 8-10 (in-person); Th. 8-10 (online)
    First lecture: October 30th.
    Please register for the lecture on this course's eCampus page.
    Registration will be possible from October 22, 10 am, until November 7, 10 am.
    The password is "Grothendieck".

    Seminar zur Algebraischen Geometrie (Modul S2A1); Nr. 611102001
    Prof. Huybrechts
    Do 16 ct - 18
    Dieses Seminar richtet sich vor allem an die Hoerer der Vorlesung Algebraic Geometry I, die planen im SS 2021 eine Bachelorarbeit in der algebraischen Geometrie zu schreiben.
    Waehrend in der Vorlesung vor allem die abstrakte Sprache der Schematheorie entwickelt wird, beschaeftigt sich das Seminar mit zentralen Konstruktionen der Theorie algebraischer Varietaeten.
    Anmeldung per email an
    Eine Vorbesprechung wird es nicht geben.

    Graduate Seminar on Algebraic Geometry (S4A1): Jacobian of curves and abelian varieties; Nr. 611501002
    Dr. Yajnaseni Dutta
    Mi 16 (c.t.) - 18
    If you would like to attend the seminar, you have to sign on a list of registrations with the lecturer and have to register technically via BASIS.

    Vorlesung Selected Topics in Algebraic Geometry (V5A4): Toric Varieties; Nr. 611500220
    Dr. Alberto Cattaneo
    Mi 14 (c.t.) - 16
    Details This lecture was cancelled in summer 2020.

    Graduate Seminar on Algebraic Geometry (S4A1): Research Seminar zur Algebraischen Geometrie "Moduli spaces of K3 surfaces and hyperkähler varieties"; Nr. 611502002
    Prof. Huybrechts
    Fr 10:15 - 11:45 Uhr

    Advanced Topics in Algebraic Geometry (V5A3): Algebraic Stacks; Nr. 611500215
    Prof. Georg Oberdieck
    Mi 14 (c.t.) - 16
    Fr 14 (c.t.) - 16

    Graduate Seminar on Algebraic Geometry (S4A1): Gastvortraege zu aktuellen Ergebnissen der algebraischen und komplexen Geometrie (SAG); Nr. 611501002
    Prof. Daniel Huybrechts, Prof. Georg Oberdieck
    Donnerstag 10:30 oder nach Ankuendigung
    On Wednesday, 04.11.: Chen Jiang (SCMS, Fudan University)
    Kalender der Bonner Mathematik

    Last modified: 21.10.2020
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