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On the Vanishing Orders of Vector Fields on Fano Varieties of Picard Number 1
Published online by Cambridge University Press: 04 December 2007
Abstract
We show that the vanishing order of a non-zero vector field at a generic point of a smooth Fano variety of Picard number 1 cannot exceed the dimension of the Fano variety. Furthermore, if there exist only finitely many rational curves of minimal degree through a generic point of the Fano variety, we show that a non-zero vector field cannot vanish at a generic point of the Fano variety.
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- © 2001 Kluwer Academic Publishers
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