We study rationally connected (projective) manifolds via the concept of a model , where is a smooth rational curve on having ample normal bundle. Models are regarded from the view point of Zariski equivalence, birational on and biregular around . 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 is investigated more thoroughly. When the (ample) normal bundle of in has minimal degree, new such models are constructed via special vector bundles on . Moreover, the formal geometry of the embedding of in is analysed for some non-trivial examples.
Paltin IONESCU. Cristian VOICA. "Models of rationally connected manifolds." J. Math. Soc. Japan 55 (1) 143 - 164, January, 2003. https://doi.org/10.2969/jmsj/1196890847