In abstract algebra, multiplicity theory concerns the multiplicity of a module M at an ideal I (often a maximal ideal) The notion of the multiplicity of a module is a generalization of the degree of a projective variety. By Serre's intersection formula, it is linked to an intersection multiplicity in the intersection theory. The main focus of the theory is to detect and measure a singular point of an algebraic variety (cf. resolution of singularities). Because of this aspect, valuation theory, Rees algebras and integral closure are intimately connected to multiplicity theory.
Property | Value |
---|---|
dbo:abstract |
|
dbo:wikiPageID |
|
dbo:wikiPageLength |
|
dbo:wikiPageRevisionID |
|
dbo:wikiPageWikiLink |
|
dbp:wikiPageUsesTemplate | |
dcterms:subject | |
rdfs:comment |
|
rdfs:label |
|
owl:sameAs | |
prov:wasDerivedFrom | |
foaf:isPrimaryTopicOf | |
is dbo:wikiPageRedirects of | |
is dbo:wikiPageWikiLink of | |
is foaf:primaryTopic of |