Greuel, Gert-Martin; Hong Duc Nguyen Right simple singularities in positive characteristic. (English) Zbl 1342.14006 J. Reine Angew. Math. 712, 81-106 (2016). 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. Reviewer: Gerhard Pfister (Kaiserslautern) Cited in 2 ReviewsCited in 6 Documents MSC: 14B05 Singularities in algebraic geometry 14J17 Singularities of surfaces or higher-dimensional varieties Keywords:simple singularity; classification right equivalence; characteristic \(p\) Citations:Zbl 0715.14001 Software:classifyCeq.lib PDFBibTeX XMLCite \textit{G.-M. Greuel} and \textit{Hong Duc Nguyen}, J. Reine Angew. Math. 712, 81--106 (2016; Zbl 1342.14006) Full Text: DOI arXiv