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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

Jun-Muk Hwang
Jun-Muk Hwang
Affiliation:
Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Seoul, 130-012, Korea. E-mail: jmhwang@ns.kias.re.kr
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Abstract

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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.

Keywords

Fano varietiesvector fieldsrational curves
Type
Research Article
Information
Compositio Mathematica , Volume 125 , Issue 3 , February 2001 , pp. 255 - 262
Copyright
© 2001 Kluwer Academic Publishers