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D.4.23.5 genus
Procedure from library normal.lib (see normal_lib).
- Return:
- an integer, the geometric genus p_g = p_a - delta of the projective
curve defined by i, where p_a is the arithmetic genus.
- Note:
- genus always treats projective curves and takes projective closure if input is affine 1-dim variety.
delta is the sum of all local delta-invariants of the singularities,
i.e. dim(R'/R), R' the normalization of the local ring R of the
singularity.
genus(I,"nor") uses the normalization to compute delta. Usually genus(I,"nor")
is slower than genus(I) but sometimes not.
genus(I,"pri") starts with a primary decompsition.
Example:
| | LIB "normal.lib";
ring r=0,(x,y),dp;
ideal i=y^9 - x^2*(x - 1)^9;
genus(i);
==> 0
ring r7=7,(x,y),dp;
ideal i=y^9 - x^2*(x - 1)^9;
genus(i);
==> 0
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