Algebroid plane curves whose Milnor and Tjurina numbers differ by one or two

Abstract

In this paper we describe all irreducible plane algebroid curves, defined over an algebraically closed field of characteristic zero, modulo analytic equivalence, having the property that the difference between their Milnor and Tjurina numbers is 1 or 2. Our work extends a previous result of O. Zariski who described such curves when this difference is zero.