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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 b2 ≦ 2. Moreover, a precise classification is obtained for b2 = 2. Complete intersections of high dimension with respect to their multi-degree provide examples for the case b2 = 1. The proof of the classification result uses a general characterization of rationality, in terms of suitable covering families of rational curves.
Received: 2008-12-08
Published Online: 2010-05-31
Published in Print: 2010-July
© Walter de Gruyter Berlin · New York 2010
