Linear system of divisors: Difference between revisions

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These arose first in the form of a ''linear system'' of [[algebraic curve]]s in the [[projective plane]]. It assumed a more general form, through gradual generalisation, so that one could speak of '''linear equivalence''' of [[divisor (algebraic geometry)|divisor]]s ''D'' on a general [[Scheme (mathematics)|scheme]] or even a [[ringed space]] <math>(X, \mathcal{O}_X)</math>.<ref>[[Alexander Grothendieck|Grothendieck, Alexandre]]; Dieudonné, Jean. ''EGA IV'', 21.3.</ref>

Linear systemsystems of dimension 1, 2, or 3 are called a '''[[Pencil (mathematics)|pencil]]''', a '''net''', or a '''web''', respectively.

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