Abstract
A rational curve C in a nonsingular variety X is standard if under the normalization f : P 1 ! C X, the vector bundle f T (X) decomposes asO(2)O (1) p O q for some nonnegative integers satisfying p +q = dimX 1. For a Fano manifold X of Picard number one and a general point x 2 X, a general rational curve of minimal degree through x is standard. It has been asked whether all rational curves of minimal degree through a general point x are standard. Our main result is a negative answer to this question.
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