Functional completeness: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>EmilJ
Further reading: this is supposed to be a reference, and it's redundant at that (it's been inlined in the ref notes)
en>Qwertyus
See also: remove links to unrelated concepts
 
Line 1: Line 1:
In [[mathematics]], the '''Fulton–Hansen connectedness theorem''' is a result from [[intersection theory]] in [[algebraic geometry]], for the case of [[subvarieties]] of [[projective space]] with [[codimension]] large enough to make the intersection have components of dimension at least 1.
The person who wrote the post is called Jayson Hirano and he totally digs that name. Distributing production is how he makes a living. Ohio is where my home is but my husband wants us to transfer. To climb is something I truly enjoy performing.<br><br>Here is my webpage: clairvoyants - [http://www.january-yjm.com/xe/index.php?mid=video&document_srl=158289 go now] -
 
The formal statement is that if ''V'' and ''W'' are irreducible algebraic subvarieties of a [[projective space]] ''P'', all over an [[algebraically closed field]], and if
 
: dim(''V'') + dim (''W'') > dim (''P'')
 
in terms of the [[dimension of an algebraic variety]], then the intersection ''U'' of ''V'' and ''W'' is [[connected space|connected]].  
 
More generally, the theorem states that if <math>Z</math> is a projective variety and <math>f:Z \to P^n \times P^n</math> is any morphism such that <math>\dim f(Z) > n</math>, then <math>f^{-1}\Delta</math> is connected, where <math>\Delta</math> is the [[diagonal]] in <math>P^n \times P^n</math>. The special case of intersections is recovered by taking <math>Z = V \times W</math>, with <math>f</math> the natural inclusion.
 
==See also==
* [[Zariski's connectedness theorem]]
* [[Grothendieck's connectedness theorem]]
* [[Deligne's connectedness theorem]]
 
==References==
* {{citation|first=W.|last= Fulton|first2= J. |last2=Hansen|title=A connectedness theorem for projective varieties with applications to intersections and singularities of mappings|journal= Annals of Math. |volume=110 |year=1979|pages= 159–166|doi=10.2307/1971249|jstor=1971249|issue=1|publisher=Annals of Mathematics}}
* {{citation|first=R.|last= Lazarsfeld|title=Positivity in Algebraic Geometry|publisher= Springer|year= 2004}}
 
==External links==
* [http://www.math.unizh.ch/fileadmin/math/preprints/20-05.pdf PDF lectures withe the result as Theorem 15.3 (attributed to Faltings, also)]
 
{{DEFAULTSORT:Fulton-Hansen connectedness theorem}}
[[Category:Intersection theory]]
[[Category:Theorems in algebraic geometry]]

Latest revision as of 12:49, 25 August 2014

The person who wrote the post is called Jayson Hirano and he totally digs that name. Distributing production is how he makes a living. Ohio is where my home is but my husband wants us to transfer. To climb is something I truly enjoy performing.

Here is my webpage: clairvoyants - go now -