Bogomolov–Sommese Vanishing Theorem

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:

This result is equivalent to the statement that:

:$H^\left(X,A^ \otimes \Omega ^_ (\log D) \right) = 0$

for every complex projective snc pair $(X, D)$ and every invertible sheaf $A \in \mathrm(X)$
with $\kappa(A) > p$.

Therefore, this theorem is called the vanishing theorem.

See also

* Bogomolov–Miyaoka–Yau inequality
* Vanishing theorem (disambiguation)

Notes

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{{DEFAULTSORT:Bogomolov-Sommese vanishing theorem
Theorems in algebraic geometry
Theorems in complex geometry