Singularities of Varieties

Generalizations
A hypersurface singularity in K d is given by a squarefree power series in
K[[x 1 ,...,x d ]].
A hypersurface singularity is smooth iff its order is 1.
The order of a reducible hypersurface singularity is equal to the sum of the
orders of the components.
Any hypesurface singularity of order n is isomorphic to one defined by
an equation F ∈ K[[x 1 , ...,x d−1 ]][x d ] such that that deg xd
(F) = n and
coeff xd n(F) = 1.
VO AAG 11