Junior Geometry Seminar – Samuele Ciprietti

Abstract: Rationally connected varieties are a central class of projective algebraic varieties characterized by the presence of rational curves connecting any two general points. These varieties generalize the notion of rational varieties and play a key role in the classification of algebraic varieties, particularly in higher-dimensional birational geometry, where they generally behave better than rational varieties. In this talk, I will give a detailed introduction to these concepts and explore some of the properties that these varieties enjoy.