  A classical phase space with a suitable symplectic structure is constructed
together with functions which have Poisson brackets algebraically identical to
the Lie algebra structure of the Lie group SU(n). In this phase space we show
that the orbit of the generators corresponding to the simple roots of the Lie
algebra give rise to fibres that are complex lines containing spheres. There
are n-1 spheres on a fibre and they intersect in exactly the same way as the
Cartan matrix of the Lie algebra. This classical phase space bundle,being
compact,has a description as a variety.Our construction shows that the variety
containing the intersecting spheres is exactly the one obtained by resolving
the singularities of the variety {x_0}{x_1}-{{x_2}^n}=0 in {C^3}. A direct
connection between this singular variety and the classical phase space
corresponding to the Lie group SU(n) is thus established.
