On the Picard number of rationally quartic connected manifolds

Taku Suzuki

doi:10.1142/S0129167X14501092

On the Picard number of rationally quartic connected manifolds

Taku Suzuki^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1142/S0129167X14501092
Publication status	Published - 2014 Nov 16

Keywords

covered by lines
Picard number
rational curves
Rationally connected manifolds

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1142/S0129167X14501092

Cite this

@article{b7b108cd4a434719819b4280d305d478,

title = "On the Picard number of rationally quartic connected manifolds",

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 (-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.",

keywords = "covered by lines, Picard number, rational curves, Rationally connected manifolds",

author = "Taku Suzuki",

year = "2014",

month = nov,

day = "16",

doi = "10.1142/S0129167X14501092",

language = "English",

volume = "25",

journal = "International Journal of Mathematics",

issn = "0129-167X",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "12",

}

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

AN - SCOPUS:84929353356

VL - 25

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

IS - 12

M1 - 1450109

ER -

On the Picard number of rationally quartic connected manifolds

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this