JournalsrmiVol. 28, No. 3pp. 815–838

Rationally cubic connected manifolds II

  • Gianluca Occhetta

    Università di Trento, Povo (Trento), Italy
  • Valentina Paterno

    Università di Trento, Povo (Trento), Italy
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Abstract

We study smooth complex projective polarized varieties (X, ⁣H)(X,\!H) of dimension n2n \ge 2 which admit a dominating family VV of rational curves of HH-degree 33, such that two general points of XX may be joined by a curve parametrized by VV and which do not admit a covering family of lines (i.e., rational curves of HH-degree one). We prove that such manifolds are obtained from RCC manifolds of Picard number one by blow-ups along smooth centers. If we further assume that XX is a Fano manifold, we obtain a stronger result, classifying all Fano RCC manifolds of Picard number ρX3\rho_X \ge 3.

Cite this article

Gianluca Occhetta, Valentina Paterno, Rationally cubic connected manifolds II. Rev. Mat. Iberoam. 28 (2012), no. 3, pp. 815–838

DOI 10.4171/RMI/692