Invariants of Hypersurface Singularities in Positive Characteristic

Details Invariants of Hypersurface Singularities in Positive Characteristic Invariants of Hypersurface Singularities in Positive Characteristic

2010-05-25

arxiv.org/abs/1005.4503v3

Rev. Math. Comp. 25, 1 (2011), 61-85

Mathematics

Algebraic Geometry

Final corrected version; to appear in Revista Matematica Complutense

Scientific paper

10.1007/s13163-010-0056-1

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.

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