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Singularities of plane projective curves


Problem: Determine the type of the singularity at (0,0) of
f(x,y) = y2-2x28y-4x21y17+4x14y33-8x7y49+x56+20y65+4x49y16 ,
and check whether this is the only singularity of the corresponding complex plane projective curve C .
The algorithm proceeds as follows:
Step 1: Classify the singularity of f at (0,0) following Arnold's classification scheme, in particular, compute the local Tjurina number of f: Tlocal(f) = dimKK[x,y]<x,y>/< jacob(f), f >
Step 2: Compute the global Tjurina number of f: Tglobal(f) = dimKK[x,y]/< jacob(f), f > If Tglobal(f) = Tlocal(f) then there is no further singularity in the affine part of C.
Step 3: Consider the singularities at infinity (coordinate change).
SINGULAR code

Cambridge (U.K.) 9-8-00 http://www.singular.uni-kl.de