| Classify |
| Coding |
| Deformations |
| Equidim Part |
| Existence |
| Finite Groups |
| Flatness |
| Genus |
| Hilbert Series |
| Membership |
| Monodromy |
| Normalization |
| Primdec |
| Puiseux |
| Plane Curves |
| Solving |
| Space Curves |
| Spectrum |
| 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,
-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] )
# ( spectral numbers of
f in (a,a+1] )
|
|
| For semi-quasihomogeneous singularities: also true for intervals (a,a+1). |