Functional completeness - Revision history

en>Qwertyus: /* See also */ remove links to unrelated concepts

2014-08-25T11:49:54Z

See also: remove links to unrelated concepts

← Older revision		Revision as of 13:49, 25 August 2014
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	~~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]]~~

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)

2013-10-31T18:56:39Z

Further reading: this is supposed to be a reference, and it's redundant at that (it's been inlined in the ref notes)

← Older revision		Revision as of 20:56, 31 October 2013
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	~~The author~~ is ~~known by~~ the ~~title~~ of ~~Figures Lint~~. ~~Playing baseball~~ is the ~~pastime he will never stop performing. My family members lives in Minnesota~~ and ~~my family loves it~~. ~~My working day occupation~~ is a ~~meter reader~~.<br><br>~~my web site :: std home test -~~ [http://www.~~hotporn123~~.~~com~~/~~blog~~/~~154316 Highly recommended Webpage~~] -		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 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]]

en>ZéroBot: r2.7.1) (Robot: Removing de:Junktor#Reduzierbarkeit der Junktorenmenge, funktionale Vollständigkeit und Sheffer-Operatoren

2012-08-20T15:12:05Z

r2.7.1) (Robot: Removing de:Junktor#Reduzierbarkeit der Junktorenmenge, funktionale Vollständigkeit und Sheffer-Operatoren

New page

The author is known by the title of Figures Lint. Playing baseball is the pastime he will never stop performing. My family members lives in Minnesota and my family loves it. My working day occupation is a meter reader.<br><br>my web site :: std home test - [http://www.hotporn123.com/blog/154316 Highly recommended Webpage] -