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Existence of Singular Hypersurfaces
Problem:
Determine maximal number of
triple points of type T3,3,3
on a surface of degree 7 in
P3.
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We use the following facts:
Fact 1:
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The singularities of type T3,3,3
form a µ-constant one parameter family given by
x3+ y3+ z3+ txyz =
0, t3
-27.
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Fact 2: |
The spectrum is constant
under µ-constant deformations
and has the following semi-continuity property:
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# ( spectral numbers of all singularities of a small deformation of
f in (a,a+1] )
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# ( spectral numbers of
f in (a,a+1] )
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For semi-quasihomogeneous singularities: also true
for intervals (a,a+1).
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SINGULAR
code
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