Asian Journal of Mathematics
Volume 17 (2013)
Characterizations of projective spaces and hyperquadrics
Pages: 583 – 596
In this paper we prove that if the $r$-th tensor power of the tangent bundle of a smooth projective variety $X$ contains the determinant of an ample vector bundle of rank at least $r$, then $X$ is isomorphic either to a projective space or to a smooth quadric hypersurface. Our result generalizes Mori’s, Wahl’s, Andreatta-Wiśniewski’s and Araujo-Druel-Kovács’s characterizations of projective spaces and hyperquadrics.
algebraic geometry, rational varieties, projective spaces, quadric hypersurfaces
2010 Mathematics Subject Classification