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A classical phase space with a suitable symplectic structure is constructedtogether with functions which have Poisson brackets algebraically identical tothe Lie algebra structure of the Lie group SU(n). In this phase space we showthat the orbit of the generators corresponding to the simple roots of the Liealgebra give rise to fibres that are complex lines containing spheres. Thereare n-1 spheres on a fibre and they intersect in exactly the same way as theCartan matrix of the Lie algebra. This classical phase space bundle,beingcompact,has a description as a variety.Our construction shows that the varietycontaining the intersecting spheres is exactly the one obtained by resolvingthe singularities of the variety {x_0}{x_1}-{{x_2}^n}=0 in {C^3}. A directconnection between this singular variety and the classical phase spacecorresponding to the Lie group SU(n) is thus established.Comment: 11 pages, 2 figures, LaTe

The appearance of the resolved singular hypersurface in the classical phase space of the Lie group SU(n)