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Statements

Subject Item
dbr:Infinitely_near_point
rdf:type
dbo:Place
rdfs:label
Infinitely near point
rdfs:comment
In algebraic geometry, an infinitely near point of an algebraic surface S is a point on a surface obtained from S by repeatedly blowing up points. Infinitely near points of algebraic surfaces were introduced by Max Noether.
dct:subject
dbc:Birational_geometry dbc:Differential_calculus dbc:Nonstandard_analysis dbc:Geometry
dbo:wikiPageID
8487086
dbo:wikiPageRevisionID
1117651271
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dbr:Algebraic_surface dbr:Algebraic_geometry dbc:Geometry dbr:Real_number dbc:Differential_calculus dbr:Blowing_up dbr:Zariski–Riemann_surface dbc:Nonstandard_analysis dbr:Infinitesimal dbr:Hyperreal_number dbc:Birational_geometry
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Max Noether
dbp:first
Max
dbp:last
Noether
dbp:year
1876
dbo:abstract
In algebraic geometry, an infinitely near point of an algebraic surface S is a point on a surface obtained from S by repeatedly blowing up points. Infinitely near points of algebraic surfaces were introduced by Max Noether. There are some other meanings of "infinitely near point". Infinitely near points can also be defined for higher-dimensional varieties: there are several inequivalent ways to do this, depending on what one is allowed to blow up. Weil gave a definition of infinitely near points of smooth varieties, though these are not the same as infinitely near points in algebraic geometry.In the line of hyperreal numbers, an extension of the real number line, two points are called infinitely near if their difference is infinitesimal.
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