Pencil of plane curves
= Pencil of plane curves
Given homogeneous polynomials $F,G$ of the same degree, their pencil is the one-parameter family
$$
V(sF+tG)\subseteq\mathbb P^2,
\qquad [s:t]\in\mathbb P^1.
$$
Its total space is the <projective hypersurface> $V(sF+tG)\subseteq\mathbb P^2\times\mathbb P^1$, and projection to $[s:t]$ has these plane curves as its <fibres of a morphism>[fibres].
It is a <pencil (geometry)> whose members are plane curves.