A remark on characterizations of projective spaces among singular varieties

作者：Ballico Edoardo^*; Fontanari Claudio

来源：Results in Mathematics, 2008, 51(3-4): 197-200.

DOI：10.1007/s00025-007-0269-x

• projective space
• quadric cone
• tangent sheaf
• ample vector bundle
• log-terminal singularities

Let X be a projective variety of dimension n >= 2 with at worst log-terminal singularities and let E subset of T(X) be an ample vector bundle of rank r. By partially extending previous results due to Andreatta and Wisniewski in the smooth case, we prove that if r = n then X congruent to P(n), while if r = n - 1 and X has only isolated singularities, then either X congruent to P(n) or n = 2 and X is the quadric cone Q(2).

• 出版日期2008