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

Research output: Contribution to journal › Article

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

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Keywords

covered by lines
Picard number
rational curves
Rationally connected manifolds

ASJC Scopus subject areas

Mathematics(all)

Cite this

Suzuki, T. (2014). On the Picard number of rationally quartic connected manifolds. International Journal of Mathematics, 25(12), [1450109]. https://doi.org/10.1142/S0129167X14501092

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10.1142/S0129167X14501092