In
algebraic geometry, Le Potier's vanishing theorem is an extension of the
Kodaira vanishing theorem, on
vector bundle
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to ev ...
s. The theorem states the following
In case of r = 1, and let E is an ample (or positive) line bundle on X, this theorem is equivalent to the
Nakano vanishing theorem. Also, found another proof.
generalizes Le Potier's vanishing theorem to k-ample and the statement as follows:
gave a counterexample, which is as follows:
See also
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vanishing theorem
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Barth–Lefschetz theorem
Note
References
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Further reading
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External links
*{{Citation , last=Demailly , first=Jean-Pierre , title=Complex Analytic and Differential Geometry , url=https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/analmeth_book.pdf (OpenContent book)
Theorems in algebraic geometry
Theorems in complex geometry