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November 2013 Characterizations of projective spaces and hyperquadrics
Stéphane Druel, Matthieu Paris
Asian J. Math. 17(4): 583-596 (November 2013).


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.


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Stéphane Druel. Matthieu Paris. "Characterizations of projective spaces and hyperquadrics." Asian J. Math. 17 (4) 583 - 596, November 2013.


Published: November 2013
First available in Project Euclid: 22 August 2014

zbMATH: 1296.14038
MathSciNet: MR3152253

Primary: 14M20

Keywords: Algebraic Geometry , projective spaces , quadric hypersurfaces , rational varieties

Rights: Copyright © 2013 International Press of Boston

Vol.17 • No. 4 • November 2013
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