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July, 2012 Rationally cubic connected manifolds I: manifolds covered by lines
Gianluca OCCHETTA, Valentina PATERNO
J. Math. Soc. Japan 64(3): 941-967 (July, 2012). DOI: 10.2969/jmsj/06430941


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.


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Gianluca OCCHETTA. Valentina PATERNO. "Rationally cubic connected manifolds I: manifolds covered by lines." J. Math. Soc. Japan 64 (3) 941 - 967, July, 2012.


Published: July, 2012
First available in Project Euclid: 24 July 2012

zbMATH: 1260.14064
MathSciNet: MR2965434
Digital Object Identifier: 10.2969/jmsj/06430941

Primary: 14M22
Secondary: 14E30 , 14J40

Keywords: Rational curves , rationally connected manifolds

Rights: Copyright © 2012 Mathematical Society of Japan


Vol.64 • No. 3 • July, 2012
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