Enumerative geometry

We all know that there is exactly 1 conic through 5 general points in the plane, but as soon as we ask how many conics are tangent to 5 given smooth conics the answer is somewhat less obvious. This kind of enumerative questions has been considered since the ancient times.

Enumerative geometry is a great playground and provides plenty of concrete problems to work with, but is sometimes left out of a basic course on algebraic geometry. This reading group aims to fill the gap. We will study how to precisely formulate enumerative questions and how to use intersection theory to find the answers.

While doing that, we will incidentally learn a lot of geometry and bump into key concepts such as Chow rings, Schubert calculus, Grassmanians, Hilbert schemes and Chern classes.

Date and time info
Wednesday 09:30 - 11:00 and Thursday 13:30 - 15:00

Keywords
Algebraic geometry, 27 lines, 3264 conics, intersection theory

Prerequisites
An undergraduate course on algebraic geometry. Enthusiasm about doing exercises and about teamwork are very welcome.

Audience
MSc students, PhD students, Postdocs

Language
English