  We study the multiplicative properties of the dual of Lusztig's semicanonical
basis.The elements of this basis are naturally indexed by theirreducible
components of Lusztig's nilpotent varieties, whichcan be interpreted as
varieties of modules over preprojective algebras.We prove that the product of
two dual semicanonical basis vectorsis again a dual semicanonical basis vector
provided the closure ofthe direct sum of thecorresponding two irreducible
components is again an irreducible component.It follows that the semicanonical
basis and the canonical basiscoincide if and only if we are in Dynkin type
$A_n$ with $n \leq 4$.Finally, we provide a detailed study of the varieties of
modules over the preprojectivealgebra of type $A_5$.We show that in this case
the multiplicative properties ofthe dual semicanonical basis are controlled by
the Ringel form of a certain tubular algebra of type (6,3,2) and by
thecorresponding elliptic root system of type $E_8^{(1,1)}$.
