About: Linear system of divisors

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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 (X, OX). Linear system of dimension 1, 2, or 3 are called a pencil, a net, or a web, respectively.

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  • 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 (X, OX). 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. (en)
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  • 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 (X, OX). Linear system of dimension 1, 2, or 3 are called a pencil, a net, or a web, respectively. (en)
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  • Linear system of divisors (en)
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