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 › 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)

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10.1142/S0129167X14501092

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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.

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KW - Rationally connected manifolds

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On the Picard number of rationally quartic connected manifolds

Abstract

Keywords

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