Singular Manual: genus

| #### D.4.25.5 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

User manual for Singular version 4.3.2p4, 2023, generated by texi2html.