Algebraic geometry - Revision history

Solomon7968 at 14:57, 18 September 2025

2025-09-18T14:57:18Z

← Older revision		Revision as of 14:57, 18 September 2025
Line 7:		Line 7:
	* Should you just be an algebraist or a geometer? is like saying Would you rather be deaf or blind? If you are blind, you do not see space: if you are deaf, you do not hear, and hearing takes place in time. On the whole, we prefer to have both faculties.		* Should you just be an algebraist or a geometer? is like saying Would you rather be deaf or blind? If you are blind, you do not see space: if you are deaf, you do not hear, and hearing takes place in time. On the whole, we prefer to have both faculties.
	** [[Michael Atiyah\| Michael Atiyah]] (2000). Mathematics in the 20th Century: geometry versus algebra, Mathematics Today, 37(2), 46- 53.		** [[Michael Atiyah\| Michael Atiyah]] (2000). Mathematics in the 20th Century: geometry versus algebra, Mathematics Today, 37(2), 46- 53.
			* In the various forms of geometry ([[Differential geometry\|differential]], [[Metric geometry\|metric]], [[Affine geometry\|affine]], [[Algebraic geometry\|algebraic]]), the central object is the variety, considered as a set of points.
			** {{cite book\|author=Pierre Cartier\|title=A country of which nothing is known but the name Grothendieck and “motives”}}

	==~~See~~ ~~also~~==		==External links==
	* [[Algebra]]

	== External links ==
	{{wikipedia}}		{{wikipedia}}

35.2.157.231 at 19:15, 11 April 2025

2025-04-11T19:15:05Z

← Older revision		Revision as of 19:15, 11 April 2025
Line 6:		Line 6:
	** {{cite book\|author=James Carlson\|title=The Poincare Conjecture\|url=https://books.google.com/books?id=i0slBQAAQBAJ&pg=PA3\|date=16 October 2014\|publisher=American Mathematical Society\|isbn=978-0-8218-9865-9\|pages=3–4}}		** {{cite book\|author=James Carlson\|title=The Poincare Conjecture\|url=https://books.google.com/books?id=i0slBQAAQBAJ&pg=PA3\|date=16 October 2014\|publisher=American Mathematical Society\|isbn=978-0-8218-9865-9\|pages=3–4}}
	* Should you just be an algebraist or a geometer? is like saying Would you rather be deaf or blind? If you are blind, you do not see space: if you are deaf, you do not hear, and hearing takes place in time. On the whole, we prefer to have both faculties.		* Should you just be an algebraist or a geometer? is like saying Would you rather be deaf or blind? If you are blind, you do not see space: if you are deaf, you do not hear, and hearing takes place in time. On the whole, we prefer to have both faculties.
	** [[Michael Atiyah\| Michael Atiyah]] (~~2001~~). Mathematics in the 20th Century: geometry versus algebra, Mathematics Today, 37(2), 46- 53.		** [[Michael Atiyah\| Michael Atiyah]] (2000). Mathematics in the 20th Century: geometry versus algebra, Mathematics Today, 37(2), 46- 53.

	==See also==		==See also==

35.2.192.106: /* Quotes */

2025-04-09T13:06:29Z

Quotes

← Older revision		Revision as of 13:06, 9 April 2025
Line 5:		Line 5:
	* While the move from dimension 2 to dimension 3 appears to be the obvious step there is a sense in which one should move from 2 to 4. This comes from the consideration of complex algebraic geometry. For complex dimension 1 this theory was started by [[Niels Henrik Abel\|Abel]] and continued by [[Bernhard Riemann\|Riemann]]. For algebraic varieties of complex dimension n the real dimension is 2n, so the case n = 2 leads to 4-dimensional real manifolds. The key figures in the topology of higher-dimensional algebraic varieties were [[Solomon Lefschetz\|Lefschetz]], [[W. V. D. Hodge\|Hodge]], [[Henri Cartan\|Cartan]] and [[Jean-Pierre Serre\|Serre]]. While general algebraic geometry was one of the major developments of the second half of the 20th century, the topology of real 4-manifolds had a great surprise in store when [[Simon Donaldson]] made spectacular discoveries opening up an entirely new area.		* While the move from dimension 2 to dimension 3 appears to be the obvious step there is a sense in which one should move from 2 to 4. This comes from the consideration of complex algebraic geometry. For complex dimension 1 this theory was started by [[Niels Henrik Abel\|Abel]] and continued by [[Bernhard Riemann\|Riemann]]. For algebraic varieties of complex dimension n the real dimension is 2n, so the case n = 2 leads to 4-dimensional real manifolds. The key figures in the topology of higher-dimensional algebraic varieties were [[Solomon Lefschetz\|Lefschetz]], [[W. V. D. Hodge\|Hodge]], [[Henri Cartan\|Cartan]] and [[Jean-Pierre Serre\|Serre]]. While general algebraic geometry was one of the major developments of the second half of the 20th century, the topology of real 4-manifolds had a great surprise in store when [[Simon Donaldson]] made spectacular discoveries opening up an entirely new area.
	** {{cite book\|author=James Carlson\|title=The Poincare Conjecture\|url=https://books.google.com/books?id=i0slBQAAQBAJ&pg=PA3\|date=16 October 2014\|publisher=American Mathematical Society\|isbn=978-0-8218-9865-9\|pages=3–4}}		** {{cite book\|author=James Carlson\|title=The Poincare Conjecture\|url=https://books.google.com/books?id=i0slBQAAQBAJ&pg=PA3\|date=16 October 2014\|publisher=American Mathematical Society\|isbn=978-0-8218-9865-9\|pages=3–4}}
			* Should you just be an algebraist or a geometer? is like saying Would you rather be deaf or blind? If you are blind, you do not see space: if you are deaf, you do not hear, and hearing takes place in time. On the whole, we prefer to have both faculties.
			** [[Michael Atiyah\| Michael Atiyah]] (2001). Mathematics in the 20th Century: geometry versus algebra, Mathematics Today, 37(2), 46- 53.

	==See also==		==See also==

MathXplore: added Category:Algebraic geometry using HotCat

2024-02-29T13:20:36Z

added Category:Algebraic geometry using HotCat

← Older revision		Revision as of 13:20, 29 February 2024
Line 16:		Line 16:
	[[Category:Algebra]]		[[Category:Algebra]]
	[[Category:Geometry]]		[[Category:Geometry]]
			[[Category:Algebraic geometry\| ]]

Mgkrupa: Added {{Math quotes}}

2022-05-15T19:00:36Z

Added {{Math quotes}}

← Older revision		Revision as of 19:00, 15 May 2022
Line 11:		Line 11:
	== External links ==		== External links ==
	{{wikipedia}}		{{wikipedia}}

			{{Math quotes}}

	[[Category:Algebra]]		[[Category:Algebra]]

Ottawahitech: ==See also== * Algebra

2021-10-11T23:04:15Z

==See also== * Algebra

← Older revision		Revision as of 23:04, 11 October 2021
Line 5:		Line 5:
	* While the move from dimension 2 to dimension 3 appears to be the obvious step there is a sense in which one should move from 2 to 4. This comes from the consideration of complex algebraic geometry. For complex dimension 1 this theory was started by [[Niels Henrik Abel\|Abel]] and continued by [[Bernhard Riemann\|Riemann]]. For algebraic varieties of complex dimension n the real dimension is 2n, so the case n = 2 leads to 4-dimensional real manifolds. The key figures in the topology of higher-dimensional algebraic varieties were [[Solomon Lefschetz\|Lefschetz]], [[W. V. D. Hodge\|Hodge]], [[Henri Cartan\|Cartan]] and [[Jean-Pierre Serre\|Serre]]. While general algebraic geometry was one of the major developments of the second half of the 20th century, the topology of real 4-manifolds had a great surprise in store when [[Simon Donaldson]] made spectacular discoveries opening up an entirely new area.		* While the move from dimension 2 to dimension 3 appears to be the obvious step there is a sense in which one should move from 2 to 4. This comes from the consideration of complex algebraic geometry. For complex dimension 1 this theory was started by [[Niels Henrik Abel\|Abel]] and continued by [[Bernhard Riemann\|Riemann]]. For algebraic varieties of complex dimension n the real dimension is 2n, so the case n = 2 leads to 4-dimensional real manifolds. The key figures in the topology of higher-dimensional algebraic varieties were [[Solomon Lefschetz\|Lefschetz]], [[W. V. D. Hodge\|Hodge]], [[Henri Cartan\|Cartan]] and [[Jean-Pierre Serre\|Serre]]. While general algebraic geometry was one of the major developments of the second half of the 20th century, the topology of real 4-manifolds had a great surprise in store when [[Simon Donaldson]] made spectacular discoveries opening up an entirely new area.
	** {{cite book\|author=James Carlson\|title=The Poincare Conjecture\|url=https://books.google.com/books?id=i0slBQAAQBAJ&pg=PA3\|date=16 October 2014\|publisher=American Mathematical Society\|isbn=978-0-8218-9865-9\|pages=3–4}}		** {{cite book\|author=James Carlson\|title=The Poincare Conjecture\|url=https://books.google.com/books?id=i0slBQAAQBAJ&pg=PA3\|date=16 October 2014\|publisher=American Mathematical Society\|isbn=978-0-8218-9865-9\|pages=3–4}}

			==See also==
			* [[Algebra]]

	== External links ==		== External links ==

UDScott: added Category:Geometry using HotCat

2021-06-29T18:39:03Z

added Category:Geometry using HotCat

← Older revision		Revision as of 18:39, 29 June 2021
Line 10:		Line 10:

	[[Category:Algebra]]		[[Category:Algebra]]
			[[Category:Geometry]]

UDScott: removed Category:Mathematics; added Category:Algebra using HotCat

2021-06-29T18:38:52Z

removed Category:Mathematics; added Category:Algebra using HotCat

← Older revision		Revision as of 18:38, 29 June 2021
Line 9:		Line 9:
	{{wikipedia}}		{{wikipedia}}

	[[Category:~~Mathematics~~]]		[[Category:Algebra]]

Solomon7968: /* Quotes */

2019-05-23T11:56:12Z

Quotes

@@ Line 3: / Line 3: @@
 {{mathematics-stub}}
 ==Quotes==
 == External links ==

UDScott at 13:23, 30 March 2017

2017-03-30T13:23:05Z

← Older revision		Revision as of 13:23, 30 March 2017
Line 1:		Line 1:
	'''[[w:Algebraic geometry\|Algebraic geometry]]''' is a branch of mathematics, classically studying zeros of multivariate ~~polynomials~~.		'''[[w:Algebraic geometry\|Algebraic geometry]]''' is a branch of [[mathematics]], classically studying [[w:zero of a function\|zeros]] of [[w:multivariate polynomial\|multivariate polynomial]]s. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from [[commutative algebra]], for solving [[geometry\|geometrical problems]] about these sets of zeros.

	{{mathematics-stub}}		{{mathematics-stub}}
	==Quotes==		==Quotes==