Abstract
We study rationally connected (projective) manifolds X via the concept of a model ðX;YÞ, where Y is a smooth rational curve on X having ample normal bundle. Models are regarded from the view point of Zariski equivalence, birational on X and biregular around Y. Several numerical invariants of these objects are introduced and a notion of minimality is proposed for them. The important special case of models Zariski equivalent to ðP n ;lineÞ is investigated more thoroughly. When the (ample) normal bundle of Y in X has minimal degree, new such models are constructed via special vector bundles on X. Moreover, the formal geometry of the embedding of Y in X is analysed for some non-trivial examples.
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