Classification of singularities in positive characteristic

Beschreibung

We treat the classification hypersurface singularities in K[[x_1,., x_n]], K an algebraically closed field of characteristic $p>0$ w.r.t. right resp. contact equivalence. Arnold classified simple, unimodal and bimodal singularities w.r.t. right equivalence in the real and complex cases. The classification of simple and unimodal singularities w.r.t. contact equivalence, in complex case, was done by Giusti and Wall, and by by Greuel and Kr\"oning in positive characteristic. We start to classify singularities in positive characteristic. We completely classify right simple singularities. It is surprising that w.r.t. right equivalence and any given p>0 we have only finitely many simple singularities. A complete right classification of all univariate power series is achieved by explicit normal forms. We also start the classification of contact unimodal singularities by giving pre-normal forms. The plane curve singularities in positive characteristic are discussed in more detail.

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Hong Duc Nguyen

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