In mathematics, Fujita's conjecture is a problem in the theories of algebraic geometry and complex manifolds, unsolved as of 2013. 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 LmK is spanned by sections when m ≥ n + 1 and is very ample when m ≥ n + 2, where n is the complex dimension of M. |
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