Birationality of the tangent map for minimal rational curves. (English) Zbl 1072.14015

The authors consider a general rational curve of minimal degree on a uniruled projective variety and prove that such curve through a general point is uniquely determined by its tangent vector. They also obtain that for any uniruled projective manifold and a minimal component, the normalization of the variety of minimal rational tangents at a general point is smooth. An application to the rigidity of generically finite morphisms to Fano manifolds of Picard number 1 is given.


14E05 Rational and birational maps
14J45 Fano varieties
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