Kovács' conjecture on characterization of projective space and hyperquadrics

We prove Kovács' conjecture that claims that if the $p^{th}$ exterior power of the tangent bundle of a smooth complex projective variety contains the $p^{th}$ exterior power of an ample vector bundle then the variety is either projective space or the $p$-dimensional quadric hypersurface. We also prove a similar characterization involving symmetric powers instead of exterior powers. This provides a common generalization of Mori, Wahl, Cho-Sato, Andreatta-Wiśniewski, Kobayashi-Ochiai, and Araujo-Druel-Kovács type characterizations of such varieties.