Day 2 (April 15) @ 11:00 – 12:30 Subroom 2
On the birational classification of algebraic varieties
The classification of algebraic varieties is one of the central questions and guiding problems in algebraic geometry. For smooth complex projective curves we have a very satisfactory classification in terms of the genus that leads to three main types of curves: the projective line, elliptic curves, and curves of general type. I will explain how, thanks to the so-called Minimal Model Program, it is possible to recover this trichotomy for higher dimensional varieties and obtain three main pure types: Fano varieties, Calabi-Yau and canonically polarised varieties. I will conclude explaining some current research questions inspired by the geometry of Fano varieties.