  Green and Griffiths have introduced several notions of singularities
associated with normal functions, especially in connection with middle
dimensional primitive Hodge classes. In this note, by using the more elementary
aspects of the Decomposition Theorem, we define global and local singularities
associated with primitive middle dimensional cohomology classes and by using
the Relative Hard Lefschetz Theorem, we show that these singularities detect
the global and local triviality of the primitive class. In a final section, we
write-up a classical inductive argument relating the Hodge conjecture to the
local non-vanishing of primitive classes.
