sentences:  An example is given by the map from the affine plane "A"2 to the conical singularity "x"2 + "y"2 = "z"2 taking ("X","Y") to (2"XY", "X"2 − "Y"2, "X"2 + "Y"2).The "XY"-plane is already nonsingular so should not be changed by resolution, and any resolution of the conical singularity factorizes through the minimal resolution given by blowing up the singular point.However the rational map from the "XY"-plane to this blowup does not extend to a regular map.