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A Morphism of Intersection Homology and Hard Lefschetz

**Andrzej Weber**

13 pages

We consider a possibility of the existence of intersection homology
morphism, which would be associated to a map of analytic varieties. We
assume that the map is an inclusion of codimension one. Then the existence
of a morphism follows from Saito's decomposition theorem. For varieties
with conical singularities we show, that the existence of intersection
homology morphism is exactly equivalent to the validity of Hard Lefschetz
Theorem for links. For varieties with arbitrary analytic singularities we
extract a remarkable property, which we call Local Hard Lefschetz.