Nori's variety and its singularities.

The moduli space of representations of a fixed dimension $n ge 2$ of the free associative algebra is a singular algebraic variety.
M.V. Nori has developed an approach to desingularise it. For
n=2, Nori's construction yields indeed a desingularization. We
will describe its homology and the structure of the fibres of the
desingularisation morphism. For n>2, Nori's variety is no longer
smooth. To understand its singularities, we study inside the variety
of all n^2-dimensional algebras the orbit closure of the algebra of
nxn matrices under the action of GL(n^2). For n = 3 we
will determine the singular locus of this orbit closure.