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 |
|---|---|
| Article number | 1450109 |
| Journal | International Journal of Mathematics |
| Volume | 25 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2014 Nov 16 |
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Keywords
- covered by lines
- Picard number
- rational curves
- Rationally connected manifolds
ASJC Scopus subject areas
- Mathematics(all)
Cite this
On the Picard number of rationally quartic connected manifolds. / Suzuki, Taku.
In: International Journal of Mathematics, Vol. 25, No. 12, 1450109, 16.11.2014.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the Picard number of rationally quartic connected manifolds
AU - Suzuki, Taku
PY - 2014/11/16
Y1 - 2014/11/16
N2 - 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 (-KX · ) ≥ 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.
AB - 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 (-KX · ) ≥ 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.
KW - covered by lines
KW - Picard number
KW - rational curves
KW - Rationally connected manifolds
UR - http://www.scopus.com/inward/record.url?scp=84929353356&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84929353356&partnerID=8YFLogxK
U2 - 10.1142/S0129167X14501092
DO - 10.1142/S0129167X14501092
M3 - Article
VL - 25
JO - International Journal of Mathematics
JF - International Journal of Mathematics
SN - 0129-167X
IS - 12
M1 - 1450109
ER -