Английская Википедия:Bogomolov–Sommese vanishing theorem

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In algebraic geometry, the Bogomolov–Sommese vanishing theorem is a result related to the Kodaira–Itaka dimension. It is named after Fedor Bogomolov and Andrew Sommese. Its statement has differing versions:

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This result is equivalent to the statement that:[1]

<math>H^{0}\left(X,A^{- 1} \otimes \Omega ^{p}_{X} (\log D) \right) = 0</math>

for every complex projective snc pair <math>(X, D)</math> and every invertible sheaf <math>A \in \mathrm{Pic}(X)</math> with <math>\kappa(A) > p</math>.

Therefore, this theorem is called the vanishing theorem.

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See also

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Further reading