Toric Geometry (WiSe 2026/27)

This course is 2 hours a week for the entire academic year.
This course is meant to be accessible for both masters students and
third year undergraduates (or even PhD students). The start of the
course will therefore include quite a bit of work on the basic notions
of algebraic geometry: affine varieties, zariski topology, projective
varieties and morphisms between these. Once those concepts have been
established, we will define toric varieties and see some simple
examples. We will discuss the group structure on these examples and
finally introduce the notion of an associated fan. This is a simple
combinatorial object which encodes the information of the toric
variety.
I will adapt the scope of the course to people’s understanding, but we
will aim to at least show a criterion for smoothness and properness of
a toric variety. If time permits we will talk about blow-ups.