= Kodaira vanishing theorem
{wiki=Kodaira_vanishing_theorem}
The Kodaira vanishing theorem is a fundamental result in algebraic geometry, named after Kunihiko Kodaira. It provides important information about the cohomology of certain types of sheaves on smooth projective varieties. \#\#\# Statement of the Theorem In its classical form, the Kodaira vanishing theorem can be stated as follows: Let \\( X \\) be a smooth projective variety over the complex numbers, and let \\( L \\) be an ample line bundle on \\( X \\).
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