Sommersemester 2020: Vorlesung Algebraic Curves

Dr. Mara Ungureanu


  • Wann und wo: Due to the ongoing health crisis and as per university regulations, the course will take place exclusively online in the period May 11 - July 31. The plan is to use a combination of asynchronous (recorded videos of the lecture) and synchronous (weekly Q&A sessions) teaching.
  • The videos of the lectures will be made available on ILIAS Tuesdays and Thursdays, at 12pm at the latest. You will need a password which is communicated to the participants via HISinOne.
  • The Q&A session is scheduled on Thursdays at 12:15, in keeping with the pre-Corona timetable. We will use the BigBlueButton platform supported by our department. Simply access SR 127 here. You will need a password which will also be communicated via HISinOne. The first meeting is on May 14.
  • HISinOne registration: Please sign up on HISinOne if you are interested in the lecture so you may have access to the course material.
  • In the week of 13 - 17 July the Q&A session and the exercise class are swapped! The Q&A will take place on 14.07 and the exercise class on 16.07 at the usual times and places.

Four decades ago David Mumford wrote that 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! ..."
The purpose of this course is to introduce students with some commutative algebra background to modern algebraic geometry via the theory of algebraic curves and without excessive prerequisites. Algebraic curves are the algebraic counterparts of Riemann surfaces and constitute a very rich topic with connections to number theory, representation theory, complex analysis, and mathematical physics. Special emphasis will be placed on examples and on developing intuition for how the abstract language of commutative algebra can be used to express geometric ideas. Topics covered include: linear series on curves, intersection theory, and the Riemann-Roch problem.




  • The exercise class will take place on Tuesdays between 12-14 on BigBlueButton. Simply access SR 127 here. The first session will be in the second week of the semester i.e. on the 19th of May.
  • Note that swap in the week 13 - 17 July with the Q&A session!
  • The exercise sheet can be found here: [tex] [pdf] (New exercises will be added to the back of the file each week.)
More organisational details will be given in the first week of the semester.


Die für Ihren Studiengang geltenden Regelungen zu Studien- und Prüfungsleistungen entnehmen Sie bitte dem jeweiligen Modulhandbuch. Die Voraussetzung für den Erhalt der Studienleistung ist die aktive Teilnahme an der Übungsgruppe, und aktive Teilnahme bedeutet:
  • Vorrechnen - Sie müssen mindestens zwei Übungsaufgaben im Rahmen der Übungen präsentieren.
  • Hausaufgaben - Sie müssen die beiden präsentierten Übungsaufgaben schriftlich ausarbeiten, einreichen und mindestens die Bewertung "bestanden" erreichen.
In einigen Studiengängen wird zusätzlich das Bestehen eines Abschlusstestes gefordert.


Voraussetzung für den Erhalt der Prüfungsleistung ist in der Regel das Bestehen der mündlichen Prüfung. Die für Ihren Studiengang geltenden Regelungen zu Studien- und Prüfungsleistungen entnehmen Sie bitte dem jeweiligen Modulhandbuch.

Mündliche oder schriftliche Prüfungen und Abschlusstests

Zeitpunkt der Prüfungen und Abschlusstests: 15. September 2020; die genaue Terminvergabe für die eventuellen 30-minütigen Prüfungen und 20-minütigen Abschlusstests erfolgt nach Ablauf der Anmeldefrist