= General position for projective lines
Distinct lines in the <projective plane> are in general position when no three are concurrent. Their union is a <reduced plane curve> with exactly $\binom d2$ <singular points>, all ordinary pairwise crossings, if there are $d$ lines. An explicit family is $y=t_i x+t_i^2z$ for distinct complex $t_i$: the intersection of the $i$th and $j$th lines is $[-t_i-t_j:-t_it_j:1]$, and substituting it into a third equation gives $-(t_k-t_i)(t_k-t_j)\ne0$.
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