  A complex algebraic variety X defined over the real numbers is called an
M-variety if the sum of its Betti numbers (for homology with closed supports
and coefficients in Z/2) coincides with the corresponding sum for the real part
of X. It has been known for a long time that any nonsingular complete toric
variety is an M-variety. In this paper we consider whether this remains true
for toric varieties that are singular or not complete, and we give a positive
answer when the dimension of X is less than or equal to 3.
