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High Quality Content by WIKIPEDIA articles! A pencil is a family of geometric objects, such as lines, that have a common property, such as passage through a given line in a given plane. In more technical language, a pencil is the special case of a linear system of divisors in which the parameter space is a projective line. In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometry notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.