  We bring examples of toric varieties blown up at a point in the torus that do
not have finitely generated Cox rings. These examples are generalizations of
previous work where toric surfaces of Picard number 1 were studied. In this
article we consider toric varieties of higher Picard number and higher
dimension. In particular, we bring examples of weighted projective 3-spaces
blown up at a point that do not have finitely generated Cox rings.
