A Remark on Characterizations of Projective Spaces among Singular Varieties

Author： Ballico Edoardo  

Publisher： Springer Publishing Company

ISSN： 1422-6383

Source： Results in Mathematics, Vol.51, Iss.3-4, 2008-03, pp. : 197-200

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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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