Abstract
In this paper, we study structures of smooth complex projective polarized manifolds (X, H) of dimension n ≥ 2 which are rationally connected with respect to a family of H-degree four. Under the assumption (-K<inf>X</inf> · ) ≥ n + 3, we prove that, with two kinds of exceptions, the Picard number of X is at most four and X is covered by rational curves of H-degree one. In addition, we provide a classification in case n = 2.
Original language | English |
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Article number | 1450109 |
Journal | International Journal of Mathematics |
Volume | 25 |
Issue number | 12 |
DOIs | |
Publication status | Published - 2014 Nov 16 |
Keywords
- covered by lines
- Picard number
- rational curves
- Rationally connected manifolds
ASJC Scopus subject areas
- Mathematics(all)