Rational curves play a crucial role in the study of algebraic varieties and finding methods to construct them is a challenging task for modern algebraic geometers.
In this talk I will explain Mori’s technique of bend and break, which gives a recipe to cook up rational curves based on the canonical class, and outline some of its consequence in higher dimensional birational geometry.
As an application of this technique I will show that any smooth Fano variety is covered by rational curves.