Journal of the Mathematical Society of Japan

Rationally cubic connected manifolds I: manifolds covered by lines

Gianluca OCCHETTA and Valentina PATERNO

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Abstract

In this paper we study smooth complex projective polarized varieties (X,H) of dimension n ≥ 2 which admit a covering family V of rational curves of degree 3 with respect to H such that two general points of X may be joined by a curve parametrized by V, and such that there is a covering family of rational curves of H-degree one.

We prove that the Picard number of these manifolds is at most three, and that, if equality holds, (X,H) has an adjunction theoretic scroll structure over a smooth variety.

Article information

Source
J. Math. Soc. Japan, Volume 64, Number 3 (2012), 941-967.

Dates
First available in Project Euclid: 24 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1343133750

Digital Object Identifier
doi:10.2969/jmsj/06430941

Mathematical Reviews number (MathSciNet)
MR2965434

Zentralblatt MATH identifier
1260.14064

Subjects
Primary: 14M22: Rationally connected varieties
Secondary: 14J40: $n$-folds ($n > 4$) 14E30: Minimal model program (Mori theory, extremal rays)

Keywords
rationally connected manifolds rational curves

Citation

OCCHETTA, Gianluca; PATERNO, Valentina. Rationally cubic connected manifolds I: manifolds covered by lines. J. Math. Soc. Japan 64 (2012), no. 3, 941--967. doi:10.2969/jmsj/06430941. https://projecteuclid.org/euclid.jmsj/1343133750


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