Le Potier's vanishing theorem

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Template:Short description In algebraic geometry, Le Potier's vanishing theorem is an extension of the Kodaira vanishing theorem, on vector bundles. The theorem states the following[1][2][3][4][5][6][7][8][9] Template:Blockquote

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, Template:Harvtxt found another proof.

Template:Harvtxt generalizes Le Potier's vanishing theorem to k-ample and the statement as follows:Template:R

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Template:Harvtxt gave a counterexample, which is as follows:Template:R[10]

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See also

Note

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  8. ↑ Template:Harv
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  10. ↑ Template:Harv

References

Further reading

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