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Right simple singularities in positive characteristic. (English) Zbl 1342.14006

Let \(K\) be an algebraically closed field of characteristic \(p>0\). Isolated simple singularities \(f\in K[[x_1, \dots, x_n]]\) are classified with respect to right equivalence. The corresponding classification with respect to contact equivalence was done by G. M. Greuel and H. Kröning [Math. Z. 203, No. 2, 339–354 (1990; Zbl 0715.14001)]. Here the result was similar to Arnold’s classification in characteristic \(0\). In case of right equivalence it turns out that there are only finitely many simple singularities.
The classification is based on the generalization of the notion of modality to the algebraic setting. It is proved that the modality is semicontinuous in any characteristic.

MSC:

14B05 Singularities in algebraic geometry
14J17 Singularities of surfaces or higher-dimensional varieties

Citations:

Zbl 0715.14001

Software:

classifyCeq.lib
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