In algebraic geometry, Le Potier's vanishing theorem is an extension of the Kodaira vanishing theorem, on vector bundles. 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: