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Singularities of plane projective curves
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Problem: |
Determine the type of the singularity
at (0,0) of |
f(x,y) =
y2-2x28y-4x21y17+4x14y33-8x7y49+x56+20y65+4x49y16 ,
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and check whether this is the only singularity of the corresponding
complex plane projective curve C .
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The algorithm proceeds as follows:
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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
>
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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.
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Step 3: |
Consider the singularities at infinity (coordinate change).
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SINGULAR
code
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