Fujita conjecture

In mathematics, Fujita's conjecture is a problem in the theories of algebraic geometry and complex manifolds, unsolved as of 2017. It is named after Takao Fujita, who formulated it in 1985.

In complex manifold theory, the conjecture states that for a positive holomorphic line bundle L on a compact complex manifold M with canonical line bundle K, then

is spanned by sections when

and is very ample when

where n is the complex dimension of M.