Linear system of divisors

In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.

These arose first in the form of a linear system of algebraic curves in the projective plane. It assumed a more general form, through gradual generalisation, so that one could speak of linear equivalence of divisors D on a general scheme or even a ringed space ${\displaystyle (X,{\mathcal {O}}_{X})}$.^[1]

Linear systems of dimension 1, 2, or 3 are called a pencil, a net, or a web, respectively.

A map determined by a linear system is sometimes called the Kodaira map.