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Models of rationally connected manifolds. (English) Zbl 1084.14052
A model (of rationally connected manifolds) is a pair $$(X,Y)$$ where $$X$$ is a projective manifold and $$Y\subset X$$ is a smooth rational curve with ample normal bundle in $$X$$. Two models $$(X,Y)$$ and $$(X',Y')$$ are said to be Zariski equivalent if there exists a birational isomorphism $$\phi: X \to X'$$ which is biregular on open subsets containing $$Y$$ and $$Y'$$ and such that $$\phi(Y)=Y'$$.
In this paper the authors study the models from the point of view of Zariski equivalence. In particular they analyze models Zariski equivalent to $$(X,Y)$$ where either $$X$$ is a projective space and $$Y$$ is a line or $$X ={\mathbb P}(E)$$ is a projective bundle over a smooth curve and $$Y$$ is a quasi-line.

##### MSC:
 14M99 Special varieties 14E05 Rational and birational maps
##### Keywords:
model; rationally connected
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