Effective Freeness of Adjoint Line Bundles

This note shows how two existing approaches to providing effective (quadratic) bounds for the freeness of adjoint line bundles can be linked to establish a new effective bound which approximately differs from the linear bound conjectured by Fujita only by a factor of the cube root of the dimension of the underlying manifold. As an application, a new effective statement for pluricanonical embeddings is derived.

2000 Mathematics Subject Classification: 14C20, 14F17, 14B05.

Keywords and Phrases: adjoint linear system -- vanishing theorem -- Fujita conjecture.

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