150 research outputs found
Some remarks on the planar Kouchnirenko's Theorem
We consider different notions of non-degeneracy, as introduced by
Kouchnirenko (NND), Wall (INND) and Beelen-Pellikaan (WNND) for plane curve
singularities and introduce the new notion of weighted
homogeneous Newton non-degeneracy (WHNND). It is known that the Milnor number
resp. the delta-invariant can be computed by explicit formulas
resp. from the Newton diagram of if is NND resp.
WNND. It was however unknown whether the equalities resp.
can be characterized by a certain non-degeneracy condition on
and, if so, by which one. We show that resp.
is equivalent to INND resp. WHNND and give some applications and interesting
examples related to the existence of "wild vanishing cycles". Although the
results are new in any characteristic, the main difficulties arise in positive
characteristic.Comment: 23 pages, 2 figures. Final versio
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