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.