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Geometric Genus of Projective
Curves -
SINGULAR
Example
LIB "normal.lib";
ring r=32003,(x,y,z,w,u),dp;
ideal i=x2+y2+z2+w2+u2,x3+y3+z3,z4+w4+u4; // a curve in P^4
genus(i);
To obtain more information on the performed computations, you should
raise the printlevel:
printlevel=3;
genus(i);
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==>
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The ideal of the projective curve:
J[1]=x2+y2+z2+w2+u2
J[2]=xy2-y3+xz2-z3+xw2+xu2
J[3]=z4+w4+u4
J[4]=y4+16001xyz2+y2z2-16001xz3-16001yz3+16001xyw2+y2w2+z2w2+16001xyu2+y2u2+z2u2+w2u2
The coefficients of the Hilbert polynomial: -48,24
arithmetic genus: 49
degree: 24
the projected curve:
10889x24-4693x22y2-3594x20y4 ... many terms ... -5931x2t22-15448y2t22-7101yt23+t24
the arithmetic genus of the plane curve: 253
analyse the singularities
......
many data
......
The projected plane curve has locally:
singularities: 204
branches: 408
nodes: 204
cusps: 0
Tjurina number: 204
Milnor number: 204
delta of the projected curve: 204
delta of the curve: 0
genus: 49
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