sentences:  There are algorithms that work by blowing up the "worst" singular points in some sense, such as , but this example shows that the definition of the "worst" points needs to be quite subtle.For more complicated singularities, such as "x"2 = "y""m""z""n" which is singular along "x" = "yz" =0, blowing up the worst singularity at the origin produces the singularities "x"2 = "y""m"+"n"−2"z""n" and "x"2 = "y""m""z""m"+"n"−2 which are worse than the original singularity if "m" and "n" are both at least 3.After the resolution the total transform, the union of the strict transform, "X", and the exceptional divisors, is a variety with singularities of the simple normal crossings type.