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Problem: Determine maximal number of triple points of type T3,3,3 on a surface of degree 7 in P3.

We use the following facts:
Fact 1: The singularities of type T3,3,3 form a µ-constant one parameter family given by
x3+ y3+ z3+ txyz = 0, t3 
eq -27.
Fact 2: The spectrum is constant under µ-constant deformations and has the following semi-continuity property:
  # ( spectral numbers of all singularities of a small deformation of f in (a,a+1] )
\leq   # ( spectral numbers of f in (a,a+1] )
For semi-quasihomogeneous singularities: also true for intervals (a,a+1).
SINGULAR code

KL, 06/03 http://www.singular.uni-kl.de