This isn’t the topic you want to study on your flight back home, however blow-ups are a key tool in algebraic geometry: several problems can be solved just with a finite number of blow-ups.
The aim of this talk is to give an introduction to this technique. We’ll focus our attention on the blow-up of a smooth point on a smooth surface.
We’ll try to present a decent amount of examples and introduce some applications, as the resolution of singularities of an embedded curve.