Screw theory - Revision history

en>Materialscientist: Reverted 1 edit by 94.187.17.50 identified as test/vandalism using STiki

2014-12-14T10:43:54Z

Reverted 1 edit by 94.187.17.50 identified as test/vandalism using STiki

← Older revision		Revision as of 12:43, 14 December 2014
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en>Wavelength: inserting 2 hyphens: —> "three-dimensional" [2 instances]—wikt:three-dimensional

2014-02-26T02:12:06Z

inserting 2 hyphens: —> "three-dimensional" [2 instances]—wikt:three-dimensional

← Older revision		Revision as of 04:12, 26 February 2014
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	In [[mathematics]], a '''quasi-projective variety''' in [[algebraic geometry]] is a locally closed subset of a [[projective variety]], i.e., the intersection inside some [[projective space]] of a [[Zariski-open]] and a [[Zariski-closed]] subset. A similar definition is used in [[scheme theory]], where a ''quasi-projective scheme'' is a locally closed [[subscheme]] of some projective space.<ref>[http://eom.springer.de/q/q076660.htm Quasi-projective scheme - Encyclopedia of Mathematics]</ref>

	~~==Relationship to affine varieties==~~

	An [[~~affine space~~]] ~~is a Zariski-open subset of~~ a [[~~projective space~~]], and ~~since any closed affine subset <math> U<~~/~~math> can~~ be ~~expressed as~~ an ~~intersection~~ of ~~the [[Homogeneous polynomial#Homogenization\|projective completion]]~~ <~~math~~>~~\bar{U}~~<~~/math~~> ~~and the affine space embedded~~ in ~~the projective space, this implies that any~~ [~~[affine variety]~~] is ~~quasiprojective~~. ~~There are [[locally closed~~]~~] subsets of projective space that~~ are not ~~affine, so that quasi-projective is more general than affine~~. ~~Taking the complement of a single point in projective space of dimension at least 2 gives a non~~-~~affine quasi~~-~~projective variety~~. ~~This is also an example of a quasi-projective variety that is neither affine nor projective.~~		As there's higher crime rate how to connect [http://Wiki.Fantasticgroup.co/index.php/Seven_Effective_Ways_To_Get_More_Out_Of_Honeywell_Home_Security cctv camera] to dvr and associated threat for your organization, you'd probably like to spend some income generally - [http://www.tulahistory.com/go.php?http://cctvdvrreviews.com www.tulahistory.com] - along with put money into [http://Wikicharities.org/index.php?title=No_More_Mistakes_With_Svat_8_Channel_Dvr DVR card]. In earlier times protection camera [http://thehotspots.co.za/members/dekuyturrenti/activity/251975/ arrangements] are actually monitored by having a separate [http://www.aif.ua/go.php?http://cctvdvrreviews.com cctv dvr mac] monitor located for the premises the place that the [http://Wikicharities.org/index.php?title=No_More_Mistakes_With_Svat_8_Channel_Dvr cameras] and DVR are pinpointed. Cctv dvr for sale The Swann DVR-8900 may [http://gf2.gameflier.com/func/actionRewriter.aspx?fid=G0004&url=http%3A//cctvdvrreviews.com ganz cctv dvr software] be the newest of the DVRs and is available by having 4, 8 or 16 BNC online video hookups suggesting you get an alternative of either a 4, 8 or 16 camera DVR.<br><br>Having a CCTV alarm system in place will be [http://Wikicharities.org/index.php?title=No_More_Mistakes_With_Svat_8_Channel_Dvr capable] to give you peace of mind your property is going [http://generation-nt.com/go/?url=http://cctvdvrreviews.com Cctv dvr system India] to be safe if you are not [http://www.bet.com/shows/106-and-park.html?ref_title=Atlanta%2BFurniture%2BAssembly&ref_url=http%3A//cctvdvrreviews.com&ref_ucid=AD157A02027A15AD0001027A15AD best home security dvr] in your property. For this you need the service of an expert locksmith who definitely are able to suggest you the places to setup CCTV plus help in perfect installation from the same.<br><br>You can practice a lot about working wireless security camera with dvr recorder on your profile from online paid dating sites ' as the concept will be the same. Do not assume that the various readers knows how to navigate your website on the order form. [http://www.propertysource.com/as.asp?aid=1234841824&curlf=5&curl=http%3A//cctvdvrreviews.com cctv dvr ireland] cctv dvr viewer for windows The pro's were a lot more than willing to provide advice and samsung galaxy valuable tips. Writing an undesirable check may be the same as stealing out of your friends, your family, or perhaps your neighbors.

	==~~Examples~~==

	Since quasi-projective varieties generalize both affine and projective varieties, they are sometimes referred to simply as ''varieties''. Varieties isomorphic to affine algebraic varieties as quasi-projective varieties are called [[affine variety\|affine varieties]~~]; similarly for projective varieties~~. For ~~example,~~ the ~~complement~~ of ~~a point~~ in the ~~affine line, i.e~~. <~~math~~>~~X=\mathbb{A}^1-0~~<~~/math~~>~~, is isomorphic to~~ the ~~zero set of~~ the ~~polynomial <math>xy-1</math> in the affine plane~~. ~~As an affine set X is~~ not ~~closed since any polynomial zero on~~ the ~~complement must be zero~~ on the ~~affine line~~. ~~For another example, the complement of any conic in projective space of dimension 2 is affine~~. ~~Varieties isomorphic to open subsets of affine varieties are called '''quasi-affine'''~~.

	~~Quasi-projective varieties are ''locally affine'' in the sense that a [[manifold]] is locally Euclidean — every point of a quasiprojective variety has a neighborhood given by an affine variety~~. ~~This yields a basis of affine sets for the Zariski topology on a quasi-projective variety.~~

	== ~~See also~~ ==
	*[[Abstract algebraic variety]~~], often synonymous with "quasi-projective variety"~~

	~~== References ==~~
	* Igor R. ~~Shafarevich~~, ~~''Basic Algebraic Geometry 1''~~, ~~Springer-Verlag 1999: Chapter 1 Section 4~~.

	~~==Notes==~~
	~~{{Reflist}}~~

	~~[[Category:Algebraic varieties]]~~

en>Rgdboer: /* Homography */ ce (displacement)

2013-11-16T21:43:27Z

Homography: ce (displacement)

← Older revision		Revision as of 23:43, 16 November 2013
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	~~Nestor~~ is the ~~title my parents gave me but I don~~'~~t like when individuals use my full title~~. ~~Kansas~~ is ~~our beginning location~~ and ~~my mothers~~ and ~~fathers live close by~~. ~~To play badminton~~ is ~~some thing he truly enjoys performing~~. ~~Interviewing~~ is ~~what she does~~.<br><br>~~My web blog :~~: [~~http~~:~~//gamesanger.com/profile/kagulley extended auto warranty companies~~]		In [[mathematics]], a '''quasi-projective variety''' in [[algebraic geometry]] is a locally closed subset of a [[projective variety]], i.e., the intersection inside some [[projective space]] of a [[Zariski-open]] and a [[Zariski-closed]] subset. A similar definition is used in [[scheme theory]], where a ''quasi-projective scheme'' is a locally closed [[subscheme]] of some projective space.<ref>[http://eom.springer.de/q/q076660.htm Quasi-projective scheme - Encyclopedia of Mathematics]</ref>

			==Relationship to affine varieties==

			An [[affine space]] is a Zariski-open subset of a [[projective space]], and since any closed affine subset <math> U</math> can be expressed as an intersection of the [[Homogeneous polynomial#Homogenization\|projective completion]] <math>\bar{U}</math> and the affine space embedded in the projective space, this implies that any [[affine variety]] is quasiprojective. There are [[locally closed]] subsets of projective space that are not affine, so that quasi-projective is more general than affine. Taking the complement of a single point in projective space of dimension at least 2 gives a non-affine quasi-projective variety. This is also an example of a quasi-projective variety that is neither affine nor projective.

			==Examples==

			Since quasi-projective varieties generalize both affine and projective varieties, they are sometimes referred to simply as ''varieties''. Varieties isomorphic to affine algebraic varieties as quasi-projective varieties are called [[affine variety\|affine varieties]]; similarly for projective varieties. For example, the complement of a point in the affine line, i.e. <math>X=\mathbb{A}^1-0</math>, is isomorphic to the zero set of the polynomial <math>xy-1</math> in the affine plane. As an affine set X is not closed since any polynomial zero on the complement must be zero on the affine line. For another example, the complement of any conic in projective space of dimension 2 is affine. Varieties isomorphic to open subsets of affine varieties are called '''quasi-affine'''.

			Quasi-projective varieties are ''locally affine'' in the sense that a [[manifold]] is locally Euclidean — every point of a quasiprojective variety has a neighborhood given by an affine variety. This yields a basis of affine sets for the Zariski topology on a quasi-projective variety.

			== See also ==
			*[[Abstract algebraic variety]], often synonymous with "quasi-projective variety"

			== References ==
			* Igor R. Shafarevich, ''Basic Algebraic Geometry 1'', Springer-Verlag 1999: Chapter 1 Section 4.

			==Notes==
			{{Reflist}}

			[[Category:Algebraic varieties]]

en>Zerodamage at 09:42, 7 August 2012

2012-08-07T09:42:27Z

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