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Linear system of divisors
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"Kodaira map" redirects here. Not to be confused with Kodaira–Spencer map from cohomology theory.
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.
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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 .[1]
Linear system 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.