Linear system of divisors: Difference between revisions

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{{redirect-distinguish2|Kodaira map|[[Kodaira–Spencer map]] from cohomology theory}}

[[File:Apollonian circles.svg|thumb|A '''linear system offersof divisors''' algebraicizes therethe classicalclassic geometricalgeometric motionnotion offersof ana [[family of curves]], as in the [[Apollonian circles]].]]

In [[algebraic geometry]], a '''linearitylinear system's offersof divisors''' issueis andan algebraicizesalgebraic generalizationsgeneralization of theirthe geometricalgeometric notion of a healthy[[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 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]] (''X'', ''O''_''X'').<ref>[[Alexander Grothendieck|Grothendieck, Alexandre]]; Dieudonné, Jean. ''EGA IV'', 21.3.</ref>