Student AG Seminar: Characterization of projective space and hyperquadrics

Projective space and hyperquadrics are amongst the simplest smooth projective varieties, and characterizing them has been a long studied problem. In this talk, I will provide an account of the existing results due to Mori, Wahl, Andreatta-Wiśniewski, Kobayashi-Ochiai, Araujo-Druel-Kovács, with particular emphasis on a result due to Druel and Paris. Furthermore, I will derive a new characterization of projective space and hyperquadrics, conjectured by Kovács, unifying  the above characterizations.