Fujita conjecture

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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^mK

is spanned by sections when

m ≥ n + 1

and is very ample when

m ≥ n + 2,

where n is the complex dimension of M.

[edit] Reference

• 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.