Pencil (geometry)
= Pencil
{disambiguate=geometry}
{wiki}
A <pencil (geometry)> is a one-parameter linear family of geometric objects. For linearly independent homogeneous <polynomials> $F,G$ of equal degree, $sF+tG=0$, indexed by $[s:t]\in\mathbb P^1$, is a <pencil (geometry)> of <plane curves> or <hypersurfaces>. Lines through a fixed point give a simple example; a <pencil of plane curves> specializes the general construction.