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- Zariskis_main_theorem abstract "In algebraic geometry, Zariski's main theorem, proved by Oscar Zariski (1943), is a statement about the structure of birational morphisms stating roughly that there is only one branch at any normal point of a variety. It is the special case of Zariski's connectedness theorem when the two varieties are birational.Zariski's main theorem can be stated in several ways which at first sight seem to be quite different, but are in fact deeply related. Some of the variations that have been called Zariski's main theorem are as follows:The total transform of a normal fundamental point of a birational map has positive dimension. This is essentially Zariski's original form of his main theorem.A birational morphism with finite fibers to a normal variety is an isomorphism to an open subset. The total transform of a normal point under a proper birational morphism is connected. A closely related theorem of Grothendieck describes the structure of quasi-finite morphisms of schemes, which implies Zariski's original main theorem.Several results in commutative algebra that imply the geometric form of Zariski's main theorem.A normal local ring is unibranch, which is a variation of the statement that the transform of a normal point is connected. The local ring of a normal point of a variety is analytically normal. This is a strong form of the statement that it is unibranch.The name \"Zariski's main theorem\" comes from the fact that Zariski labelled it as the \"MAIN THEOREM\" in Zariski (1943).".
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- Zariskis_main_theorem wikiPageWikiLink Analytically_normal_ring.
- Zariskis_main_theorem wikiPageWikiLink Category:Theorems_in_algebraic_geometry.
- Zariskis_main_theorem wikiPageWikiLink Compact_space.
- Zariskis_main_theorem wikiPageWikiLink Delignes_connectedness_theorem.
- Zariskis_main_theorem wikiPageWikiLink Finite_morphism.
- Zariskis_main_theorem wikiPageWikiLink Fulton–Hansen_connectedness_theorem.
- Zariskis_main_theorem wikiPageWikiLink Glossary_of_algebraic_geometry.
- Zariskis_main_theorem wikiPageWikiLink Grothendiecks_connectedness_theorem.
- Zariskis_main_theorem wikiPageWikiLink Quasi-finite_morphism.
- Zariskis_main_theorem wikiPageWikiLink Scheme_(mathematics).
- Zariskis_main_theorem wikiPageWikiLink Springer_Science+Business_Media.
- Zariskis_main_theorem wikiPageWikiLink Stein_factorization.
- Zariskis_main_theorem wikiPageWikiLink Theorem_on_formal_functions.
- Zariskis_main_theorem wikiPageWikiLink Unibranch_local_ring.
- Zariskis_main_theorem wikiPageWikiLink Zariskis_connectedness_theorem.
- Zariskis_main_theorem wikiPageWikiLinkText "Zariski's main theorem".
- Zariskis_main_theorem authorlink "Oscar Zariski".
- Zariskis_main_theorem first "Oscar".
- Zariskis_main_theorem first "V.I.".
- Zariskis_main_theorem id "Z/z099130".
- Zariskis_main_theorem last "Danilov".
- Zariskis_main_theorem last "Zariski".
- Zariskis_main_theorem title "Zariski theorem".
- Zariskis_main_theorem txt "yes".
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- Zariskis_main_theorem year "1943".
- Zariskis_main_theorem subject Category:Theorems_in_algebraic_geometry.
- Zariskis_main_theorem hypernym Statement.
- Zariskis_main_theorem type Theorem.
- Zariskis_main_theorem comment "In algebraic geometry, Zariski's main theorem, proved by Oscar Zariski (1943), is a statement about the structure of birational morphisms stating roughly that there is only one branch at any normal point of a variety. It is the special case of Zariski's connectedness theorem when the two varieties are birational.Zariski's main theorem can be stated in several ways which at first sight seem to be quite different, but are in fact deeply related.".
- Zariskis_main_theorem label "Zariski's main theorem".
- Zariskis_main_theorem sameAs Q8066795.
- Zariskis_main_theorem sameAs m.03cprbq.
- Zariskis_main_theorem sameAs Q8066795.
- Zariskis_main_theorem wasDerivedFrom Zariskis_main_theorem?oldid=672628958.
- Zariskis_main_theorem isPrimaryTopicOf Zariskis_main_theorem.