D.5.7.2 ModEqn

Procedure from library qhmoduli.lib (see qhmoduli_lib).

Usage:

ModEqn(f [, opt]); poly f; int opt;

Purpose:

compute equations of the moduli space of semiquasihomogeneous hypersurface singularity with principal part f w.r.t. right equivalence

Assume:

f quasihomogeneous polynomial with an isolated singularity at 0

Return:

polynomial ring, possibly a simple extension of the ground field of the basering, containing the ideal ’modid’
- ’modid’ is the ideal of the moduli space if opt is even (> 0). otherwise it contains generators of the coordinate ring R of the moduli space (note : Spec(R) is the moduli space)

Options:

1 compute equations of the mod. space,
2 use a primary decomposition
4 compute E_f0, i.e., the image of G_f0
To combine options, add their value, default: opt =7

Example:

LIB "qhmoduli.lib";
ring B   = 0,(x,y), ls;
poly f = -x4 + xy5;
def R = ModEqn(f);
setring R;
modid;
→ modid[1]=Y(5)^2-Y(4)*Y(6)
→ modid[2]=Y(4)*Y(5)-Y(3)*Y(6)
→ modid[3]=Y(3)*Y(5)-Y(2)*Y(6)
→ modid[4]=Y(2)*Y(5)-Y(1)*Y(6)
→ modid[5]=Y(4)^2-Y(2)*Y(6)
→ modid[6]=Y(3)*Y(4)-Y(1)*Y(6)
→ modid[7]=Y(2)*Y(4)-Y(1)*Y(5)
→ modid[8]=Y(3)^2-Y(1)*Y(5)
→ modid[9]=Y(2)*Y(3)-Y(1)*Y(4)
→ modid[10]=Y(2)^2-Y(1)*Y(3)