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

Hwang, Jun-Muk; Mok, Ngaiming

Asian J. Math. 8, No. 1, 51-64 (2004).

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.

Reviewer: Georgi Hristov Georgiev (Shumen)

MSC:

14E05	Rational and birational maps
14J45	Fano varieties

Keywords:

uniruled projective variety