Bloodstain pattern analysis - Revision history

en>Widr: Reverted 1 edit by 173.79.106.230 using STiki

2015-01-07T21:31:02Z

Reverted 1 edit by 173.79.106.230 using STiki

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	~~Wilber Berryhill is what his spouse loves to contact him and he completely enjoys this~~ title~~. Mississippi is exactly where his home~~ is~~. My husband doesn't like it the way I do~~ but ~~what I~~ truly ~~like [http://www~~.~~khuplaza~~.~~com/dent/14869889 psychics online] performing~~ is ~~caving but I don't have the time lately~~. My ~~working free psychic readings [[http://formalarmour.com/index.php?do=/profile-26947/info/ http://formalarmour.com]]~~ day ~~job is an info officer but I've currently utilized for another one~~.<br><br>~~Feel free to surf to~~ my web ~~page; spirit messages (~~[http://~~Www~~.~~010-5260-5333~~.~~com~~/index.php?document_srl=~~1880~~&mid=~~board_ALMP66 simply click the next internet site~~])		Hi there. Allow me start by introducing the writer, her title is Sophia Boon but she by no means truly favored that name. Invoicing is my occupation. To climb is some thing she would never give up. My wife and I live in Mississippi and I love each day residing right here.<br><br>Also visit my web blog ... authentic psychic readings [[http://Si.Dgmensa.org/xe/index.php?document_srl=48014&mid=c0102 Highly recommended Webpage]]

en>Bali88 at 01:06, 26 February 2014

2014-02-26T01:06:35Z

← Older revision		Revision as of 03:06, 26 February 2014
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	~~In [[mathematics]], a '''Lefschetz pencil'''~~ is ~~a construction in [[algebraic geometry]] considered by [[Solomon Lefschetz]], used~~ to ~~analyse the [[algebraic topology]] of an [[algebraic variety]] ''V''~~. ~~A ''pencil''~~ is ~~a particular kind of [[linear system of divisors]] on ''V'', namely a one-parameter family, parametrised by the [[projective line]]~~. ~~This means that in the case of a [[complex algebraic variety]] '~~'~~V'', a Lefschetz pencil is something~~ like ~~a [[fibration]] over~~ the ~~[[Riemann sphere]];~~ but ~~with two qualifications about singularity.~~		Wilber Berryhill is what his spouse loves to contact him and he completely enjoys this title. Mississippi is exactly where his home is. My husband doesn't like it the way I do but what I truly like [http://www.khuplaza.com/dent/14869889 psychics online] performing is caving but I don't have the time lately. My working free psychic readings [[http://formalarmour.com/index.php?do=/profile-26947/info/ http://formalarmour.com]] day job is an info officer but I've currently utilized for another one.<br><br>Feel free to surf to my web page; spirit messages ([http://Www.010-5260-5333.com/index.php?document_srl=1880&mid=board_ALMP66 simply click the next internet site])

	~~The first point comes up if we assume that ''V'' is given as a~~ [[projective variety]], and the divisors on ''V'' are [[hyperplane section]]s. Suppose given hyperplanes ''H'' and ''H''′, spanning the pencil — in other words, ''H'' is given by ''L'' = 0 and ''H''′ by ''L''′= 0 for linear forms ''L'' and ''L''′, and the general hyperplane section is ''V'' intersected with

	:~~<math>\lambda L + \mu L^\prime = 0.\ <~~/~~math>~~

	~~Then the intersection ''J'' of ''H'' with ''H''′ has [[codimension]] two. There is a [[rational mapping]]~~

	~~:<math>V \rightarrow P^1\ <~~/~~math>~~

	~~which is in fact well-defined only outside the points on the intersection of ''J'' with ''V''. To make a well-defined mapping, some [[blowing up]] must be applied to ''V''.~~

	The second point is that the fibers may themselves 'degenerate' and acquire [[Mathematical singularity\|singular points]] (where [[Bertini's lemma]] applies, the ''general'' hyperplane section will be smooth). A Lefschetz pencil restricts the nature of the acquired singularities, so that the topology may be analysed by the [[vanishing cycle]] method. The fibres with singularities are required to have a unique quadratic singularity, only.~~<ref>{{Springer\|id = m~~/~~m064700\|title = Monodromy transformation}}<~~/~~ref>~~

	~~It has been shown that Lefschetz pencils exist in [[characteristic zero~~]~~]. They apply in ways similar to,~~ but ~~more complicated than, [[Morse function]]s on [[smooth manifold]]s.~~

	~~[[Simon Donaldson]] has found a role for Lefschetz pencils in [[symplectic topology]], leading to more recent research interest in them.~~

	~~==See also==~~

	*[[Picard–Lefschetz theory]]

	~~==References==~~
	*S. K. Donaldson, '~~'Lefschetz Fibrations in Symplectic Geometry'', Doc~~. ~~Math. J. DMV Extra Volume ICM II (1998), 309-314~~
	* {{cite book \| author=P. Griffiths \| authorlink=Phillip Griffiths \| coauthors=[[~~Joe Harris (mathematician)\|J. Harris]] \| title=Principles of Algebraic Geometry \| series=Wiley Classics Library \| publisher=Wiley Interscience \| year=1994 \| isbn=0-471-05059-8 \| page=509 }}~~

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

	~~==External links==~~
	*Gompf, Robert; [http://~~www~~.ma.~~utexas.edu~~/~~users~~/~~jwilliam~~/~~Documents~~/me/~~lefschetzpencil~~.~~pdf ''What is a Lefschetz pencil?''~~]~~; ([[PDF~~]~~]) ''Notices of the American Mathematical Society'~~'; ~~vol. 52, no. 8~~ (~~September 2005).~~
	*Gompf, Robert; [http://~~www~~.~~ma.utexas~~.~~edu/users/combs/Gompf~~/~~gompf00~~.~~pdf The Topology of Symplectic Manifolds~~] ~~(PDF~~) ~~pp.10-12.~~

	~~[[Category:Geometry of divisors]]~~

en>Twinsday: /* In popular culture */

2014-01-22T11:53:00Z

In popular culture

← Older revision		Revision as of 13:53, 22 January 2014
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	~~I would like~~ to ~~introduce myself to you~~, ~~I am Andrew and my wife doesn~~'t like ~~it at all~~. It's ~~not a typical factor but what I like doing~~ is ~~to climb but I don~~'~~t have~~ the ~~time recently~~. ~~Invoicing~~ is ~~my occupation~~. ~~Alaska~~ is ~~exactly~~ where I'~~ve always been residing~~.<br><br>~~my webpage~~ ... ~~free psychic readings~~; [http://~~myoceancounty~~.~~net~~/~~groups~~/~~apply-these-guidelines-when-gardening-and-grow~~/ ~~visit~~ the ~~website~~],		In [[mathematics]], a '''Lefschetz pencil''' is a construction in [[algebraic geometry]] considered by [[Solomon Lefschetz]], used to analyse the [[algebraic topology]] of an [[algebraic variety]] ''V''. A ''pencil'' is a particular kind of [[linear system of divisors]] on ''V'', namely a one-parameter family, parametrised by the [[projective line]]. This means that in the case of a [[complex algebraic variety]] ''V'', a Lefschetz pencil is something like a [[fibration]] over the [[Riemann sphere]]; but with two qualifications about singularity.

			The first point comes up if we assume that ''V'' is given as a [[projective variety]], and the divisors on ''V'' are [[hyperplane section]]s. Suppose given hyperplanes ''H'' and ''H''′, spanning the pencil — in other words, ''H'' is given by ''L'' = 0 and ''H''′ by ''L''′= 0 for linear forms ''L'' and ''L''′, and the general hyperplane section is ''V'' intersected with

			:<math>\lambda L + \mu L^\prime = 0.\ </math>

			Then the intersection ''J'' of ''H'' with ''H''′ has [[codimension]] two. There is a [[rational mapping]]

			:<math>V \rightarrow P^1\ </math>

			which is in fact well-defined only outside the points on the intersection of ''J'' with ''V''. To make a well-defined mapping, some [[blowing up]] must be applied to ''V''.

			The second point is that the fibers may themselves 'degenerate' and acquire [[Mathematical singularity\|singular points]] (where [[Bertini's lemma]] applies, the ''general'' hyperplane section will be smooth). A Lefschetz pencil restricts the nature of the acquired singularities, so that the topology may be analysed by the [[vanishing cycle]] method. The fibres with singularities are required to have a unique quadratic singularity, only.<ref>{{Springer\|id = m/m064700\|title = Monodromy transformation}}</ref>

			It has been shown that Lefschetz pencils exist in [[characteristic zero]]. They apply in ways similar to, but more complicated than, [[Morse function]]s on [[smooth manifold]]s.

			[[Simon Donaldson]] has found a role for Lefschetz pencils in [[symplectic topology]], leading to more recent research interest in them.

			==See also==

			*[[Picard–Lefschetz theory]]

			==References==
			*S. K. Donaldson, ''Lefschetz Fibrations in Symplectic Geometry'', Doc. Math. J. DMV Extra Volume ICM II (1998), 309-314
			* {{cite book \| author=P. Griffiths \| authorlink=Phillip Griffiths \| coauthors=[[Joe Harris (mathematician)\|J. Harris]] \| title=Principles of Algebraic Geometry \| series=Wiley Classics Library \| publisher=Wiley Interscience \| year=1994 \| isbn=0-471-05059-8 \| page=509 }}

			==Notes==
			{{Reflist}}

			==External links==
			*Gompf, Robert; [http://www.ma.utexas.edu/users/jwilliam/Documents/me/lefschetzpencil.pdf ''What is a Lefschetz pencil?'']; ([[PDF]]) ''Notices of the American Mathematical Society''; vol. 52, no. 8 (September 2005).
			*Gompf, Robert; [http://www.ma.utexas.edu/users/combs/Gompf/gompf00.pdf The Topology of Symplectic Manifolds] (PDF) pp.10-12.

			[[Category:Geometry of divisors]]

en>Blethering Scot: Reverted edits by Peaches256 to last version by Anir1uph (GLOO)

2012-07-10T19:30:31Z

Reverted edits by Peaches256 to last version by Anir1uph (GLOO)

New page

I would like to introduce myself to you, I am Andrew and my wife doesn't like it at all. It's not a typical factor but what I like doing is to climb but I don't have the time recently. Invoicing is my occupation. Alaska is exactly where I've always been residing.<br><br>my webpage ... free psychic readings; [http://myoceancounty.net/groups/apply-these-guidelines-when-gardening-and-grow/ visit the website],