Normal Forms of Hypersurface Singularities in Positive Characteristic

Boubakri, Yousra; Greuel, Gert–Martin; Markwig, Thomas

doi:10.48550/arxiv.1007.0170

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2010

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“…Our principle interest is the classification of power series with respect to right respectively contact equivalence (see [BGM10]). In order to do this we need finiteness conditions and therefore we restrict to the isolated case, i.e.…”

Section: Introductionmentioning

confidence: 99%

Invariants of hypersurface singularities in positive characteristic

2010

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We study singularities f ∈ K [[x 1 , . . . , x n ]] over an algebraically closed field K of arbitrary characteristic with respect to right respectively contact equivalence, and we establish that the finiteness of the Milnor respectively the Tjurina number is equivalent to finite determinacy. We give improved bounds for the degree of determinacy in positive characteristic. Moreover, we consider different non-degeneracy conditions of Kouchnirenko, Wall and Beelen-Pellikaan in positive characteristic, and we show that planar Newton non-degenerate singularities satisfy Milnor's formula μ = 2 · δ − r + 1. This implies the absence of wild vanishing cycles in the sense of Deligne.

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Section: Introductionmentioning

confidence: 99%