Asian Journal of Mathematics

Characterizations of projective spaces and hyperquadrics

Stéphane Druel and Matthieu Paris

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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.

Article information

Source
Asian J. Math., Volume 17, Number 4 (2013), 583-596.

Dates
First available in Project Euclid: 22 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1408712343

Mathematical Reviews number (MathSciNet)
MR3152253

Zentralblatt MATH identifier
1296.14038

Subjects
Primary: 14M20: Rational and unirational varieties [See also 14E08]

Keywords
Algebraic geometry rational varieties projective spaces quadric hypersurfaces

Citation

Druel, Stéphane; Paris, Matthieu. Characterizations of projective spaces and hyperquadrics. Asian J. Math. 17 (2013), no. 4, 583--596. https://projecteuclid.org/euclid.ajm/1408712343


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