Asian Journal of Mathematics

Volume 17 (2013)

Number 4

Characterizations of projective spaces and hyperquadrics

Pages: 583 – 596

DOI: http://dx.doi.org/10.4310/AJM.2013.v17.n4.a1

Authors

Stéphane Druel (Institut Fourier, UMR 5582 du CNRS, Université Grenoble 1, Saint Martin d’Hères, France)

Matthieu Paris (Institut Fourier, UMR 5582 du CNRS, Université Grenoble 1, Saint Martin d’Hères, France)

Abstract

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.

Keywords

algebraic geometry, rational varieties, projective spaces, quadric hypersurfaces

2010 Mathematics Subject Classification

14M20

Full Text (PDF format)