DOCUMENTA MATHEMATICA, Vol. 7 (2002), 31-42

Gordon Heier

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.

Full text: dvi.gz 21 k, dvi 49 k, ps.gz 450 k, pdf 141 k.