The seminar aims to introduce several fundamental methods and tools of algebraic geometry through the study of algebraic curves.
While some prior exposure to algebraic geometry is recommended, most topics require only one or two standard introductory courses as a prerequisite.

The detailed program will be presented at the preliminary meeting. Throughout the seminar, we will intertwine the development of foundational tools with the study of specific low-genus curves.
Planned topics include:

• Riemann-Roch and Serre duality for curves,
• The Riemann-Hurwitz formula,
• Genus 0 curves and central simple algebras,
• Elliptic curves and genus 1 curves.

At the request of interested students, further topics may be added, such as curves in positive characteristic, Severi-Brauer varieties, and selected examples of algebraic surfaces.

The preliminary meeting of the seminar is on July 14 (Tuesday), 14.00, in M201.
If you are interested in attending the seminar, but cannot attend the preliminary meeting,
please contact one of the organisers, Andrea Panontin < Andrea.Panontin@ur.de > or Pavel Sechin < Pavel.Sechin@ur.de >.

• Registration for course work/examination/ECTS: FlexNow

• Presentation: Giving a seminar talk of roughly 90 minutes

• Detailed written report of the seminar talk