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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rdfs:label	Linear system of divisors (en)
rdfs:comment	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)
rdfs:seeAlso	Theorem of Bertini
foaf:depiction
dcterms:subject	Geometry of divisors
Wikipage page ID	1186886 (xsd:integer)
Wikipage revision ID	1115995700 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective plane Projective bundle Algebraic surface Pencil (mathematics) Invertible sheaf Ringed space Normal bundle Closed immersion Function field of an algebraic variety Bundle of principal parts Cayley–Bacharach theorem Weil divisor Line bundle Algebraic curve Algebraic geometry Algebraic variety Ample line bundle Brill–Noether theory Family of curves Italian school of algebraic geometry Kodaira–Spencer map Lefschetz pencil Rational function Henri Poincaré Hyperelliptic curve Geometry of divisors Birational geometry Homological algebra Picard group Free abelian group Mathematical singularity Scheme (mathematics) Riemann–Roch theorem Invertible sheaves Springer-Verlag Cartier divisor Relative Proj Numerically effective Holomorphic line bundle Kodaira–Spencer theory Trigonal curve Zariski
sameAs	Linear system of divisors Linear system of divisors Linear system of divisors
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has abstract	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)
gold:hypernym	Generalization
prov:wasDerivedFrom	wikipedia-en:Linear_system_of_divisors?oldid=1115995700&ns=0
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foaf:isPrimaryTopicOf	wikipedia-en:Linear_system_of_divisors
is Link from a Wikipage to another Wikipage of	Enumerative geometry List of algebraic geometry topics Algebraic geometry of projective spaces Pencil (geometry) Degree of an algebraic variety Net Reider's theorem Glossary of classical algebraic geometry Linear system of conics Clifford's theorem on special divisors Functor represented by a scheme Bundle of principal parts Cayley–Bacharach theorem Line at infinity Brill–Noether theory Base locus Family of curves Italian school of algebraic geometry Lefschetz pencil Projective variety Intersection theory Hyperelliptic curve cryptography K3 surface Coherent duality

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