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The singularities of algebraic plane curves over Q may be resolved into ordinary multiple points by the classical met hod of st andard quadratic t ransformat ions. The author analyzes a birational plane transformation described by Max Noether which improves upon the classical method in two ways: first, it requires no ground field extension; second, the degree of the curve it produces is an exponential factor lower than that produced by the standard method.

Noether's S-transformation simplifies curve singularities rationally