Abstract.
Let X be a projective variety of dimension n ≥ 2 with at worst log-terminal singularities and let \(E \subseteq T_X\) be an ample vector bundle of rank r. By partially extending previous results due to Andreatta and Wiśniewski in the smooth case, we prove that if r = n then \(X \cong {\mathbb{P}}^n\), while if r = n − 1 and X has only isolated singularities, then either \(X \cong {\mathbb{P}}^n\) or n = 2 and X is the quadric cone Q 2.
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It is a pleasure to thank Marco Andreatta and Jarek Wiśniewski for nice conversations on the subject of the present paper. This research was partially supported by M.I.U.R. (Italy).
Received: April 20, 2006. Revised: April 5, 2007.
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Ballico, E., Fontanari, C. A Remark on Characterizations of Projective Spaces among Singular Varieties. Result. Math. 51, 197–200 (2008). https://doi.org/10.1007/s00025-007-0269-x
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DOI: https://doi.org/10.1007/s00025-007-0269-x