抄録
We give a geometric interpretation of the minimal generating system of the semi-group defined by a rational polyhedral cone in any dimension, via a natural bijection with the set of essential divisors of equivariant desingularizations of the toric variety associated to the cone. We prove, for varieties of dimension three, the existence of a desingularization associated to a regular fan whose edges contain the elements of the minimal generating system, its uniqueness for canonical toric varieties of index at least two, and the uniqueness in general up to flops. We give an example of non-existence of such desingularizations in dimension four.
