Bogomolov–Sommese vanishing theorem

Template:Short description Template:Distinguish 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:^[1]

H^{0} (X, A^{- 1} \otimes Ω_{X}^{p} (\log D)) = 0

for every complex projective snc pair $(X, D)$ and every invertible sheaf $A \in P i c (X)$ with $κ (A) > p$ .

Therefore, this theorem is called the vanishing theorem.

Notes