Conic-connected manifolds

By Paltin Ionescu, Francesco Russo. 2007

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Abstract We study a particular class of rationally connected manifolds, , such that two general points x, x′ ∈ X may be joined by a conic contained in X. We prove that these manifolds are Fano, with b 2 ≦ 2. Moreover, a precise classification is obtained for b 2 = 2. Complete intersections of high dimension with respect to their multi-degree provide examples for the case b 2 = 1. The proof of the classification result uses a general characterization of rationality, in terms of suitable covering families of rational curves.

Subfields: Computational Mechanics, Geometry and Topology, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/28179895de017a787197277a7645cf4f6bf9e2da