Invariants of Hypersurface Singularities in Positive Characteristic

Abstract

We study singularities f in 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 mu=2 delta-r+1. This implies the absence of wild vanishing cycles in the sense of Deligne.

Final corrected version; to appear in Revista Matematica Complutense

References in corpus (1)

• Invariants of Hypersurface Singularities in Positive Characteristic

Cited by in corpus (9)

• Invariants of Hypersurface Singularities in Positive Characteristic
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• Links of singularities of inner non-degenerate mixed functions
• On the Milnor formula in arbitrary characteristic
• The Milnor number of plane irreducible singularities in positive characteristic
• Classification of Unimodal Parametric Plane Curve Singularities in Positive Characteristic
• The Splitting Lemma in any Characteristic
• An algebraic proof of the Milnor-Orlik theorem
• Conjectures on stably Newton degenerate singularities