GEOMETRIC AND ANALYTICAL ASPECTS OF ANYONS

We consider quantum systems of n indistinguishable spinless particles, constrained to closed compact surfaces and satisfying fractional stat istics (anyons). We question the traditional choice of a configuration space, and show that a theory maintaining the diagonal is possible. S uch a theory leads naturally to questions in algebraic geometry involv ing desingularization of certain algebraic varieties. The desingulariz ation induce the possibility of an ''exotic exclusion principle'' for anyons, wherein multiple occupancy is not excluded in general.