Line bundles on complex tori and a conjecture of Kodaira

Details Line bundles on complex tori and a conjecture of Kodaira Line bundles on complex tori and a conjecture of Kodaira

2002-12-18

arxiv.org/abs/math/0212243v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

A famous conjecture attributed to Kodaira asks whether any compact Kaehler manifold can be approximated by projective manifolds. We confirm this conjecture on projectivized direct sums of three line bundles on three-dimensional complex tori which appears rather surprising in view of expected dimensions of certain families of tori. We also discuss possible counter examples.

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