Fujita conjecture

In mathematics, Fujita's conjecture is a problem in the theories of algebraic geometry and complex manifolds, unsolved as of 2005.

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

:"L"^"m""K"

is spanned by sections when

:"m" ≥ "n" + 1

and is very ample when

:"m" ≥ "n" + 2,

where "n" is the complex dimension of "M".

References

*T. Fujita, "On polarized manifolds whose adjoint bundles are not semipositive", Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, 1987, pp. 167–178.