Elliptic-Parabolic-Hyperbolic trichotomy in mathematics - 편집 역사

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@@ 7번째 줄: / 7번째 줄: @@
 ==algebraic geometry==
-* Let $X$ be a smooth complex projective variety. There are three main types of varieties.
+* Let <math>X</math> be a smooth complex projective variety. There are three main types of varieties.
 * Not every variety is of one of these three types, but minimal model theory relates every variety to one of these extreme types
-# Fano. This means that $−K_X$ is ample. (We recall the definition of ampleness in section 2.)
+# Fano. This means that <math>−K_X</math> is ample. (We recall the definition of ampleness in section 2.)
-# Calabi-Yau. We define this to mean that $K_X$ is numerically trivial.
+# Calabi-Yau. We define this to mean that <math>K_X</math> is numerically trivial.
-# ample canonical bundle. This means that $K_X$ is ample; it implies that $X$ is of general type.”
+# ample canonical bundle. This means that <math>K_X</math> is ample; it implies that <math>X</math> is of general type.”
-* Here, for $X$ of complex dimension $n$, the canonical bundle $K_X$ is the line bundle $\Omega^n_X$ of $n$-forms.
+* Here, for <math>X</math> of complex dimension <math>n</math>, the canonical bundle <math>K_X</math> is the line bundle <math>\Omega^n_X</math> of <math>n</math>-forms.
-* We write $−K_X$ for the dual line bundle $K^∗_X$, the determinant of the tangent bundle.
+* We write <math>−K_X</math> for the dual line bundle <math>K^∗_X</math>, the determinant of the tangent bundle.

← 이전 판	2020년 11월 13일 (금) 15:53 판
1번째 줄:	1번째 줄:
	+	==introduction==
	+	* spherical-Euclidean-hyperbolic
	+	* finite-affine-indefinite
	+	* {{수학노트\|url=리만_사상_정리_Riemann_mapping_theorem_and_the_uniformization_theorem}}
	+	* {{수학노트\|url=이차곡선(원뿔곡선)}}

	+
	+	==algebraic geometry==
	+	* Let $X$ be a smooth complex projective variety. There are three main types of varieties.
	+	* Not every variety is of one of these three types, but minimal model theory relates every variety to one of these extreme types
	+	# Fano. This means that $−K_X$ is ample. (We recall the definition of ampleness in section 2.)
	+	# Calabi-Yau. We define this to mean that $K_X$ is numerically trivial.
	+	# ample canonical bundle. This means that $K_X$ is ample; it implies that $X$ is of general type.”
	+	* Here, for $X$ of complex dimension $n$, the canonical bundle $K_X$ is the line bundle $\Omega^n_X$ of $n$-forms.
	+	* We write $−K_X$ for the dual line bundle $K^∗_X$, the determinant of the tangent bundle.
	+
	+
	+	==memo==
	+	* http://mathoverflow.net/questions/120612/trichotomies-in-mathematics
	+
	+
	+	==articles==
	+	* Terragni, T. “Data about Hyperbolic Coxeter Systems.” arXiv:1503.08764 [math], March 30, 2015. http://arxiv.org/abs/1503.08764.
	+	* Rastegar, Arash. ‘EPH-Classifications in Geometry, Algebra, Analysis and Arithmetic’. arXiv:1503.07859 [math], 26 March 2015. http://arxiv.org/abs/1503.07859.
	+	* Totaro, Burt. ‘Algebraic Surfaces and Hyperbolic Geometry’. ArXiv E-Prints 1008 (1 August 2010): 3825.
	+
	+
	+
	+	[[분류:abstract concepts]]
	+	[[분류:migrate]]

← 이전 판		2020년 11월 13일 (금) 15:53 판
1번째 줄:		1번째 줄:
−	~~==introduction==~~
−	* spherical-Euclidean-hyperbolic
−	* finite-affine-indefinite
−	* {{수학노트\|url=리만_사상_정리_Riemann_mapping_theorem_and_the_uniformization_theorem}}
−	* {{수학노트\|url=이차곡선(원뿔곡선)}}

−
−	~~==algebraic geometry==~~
−	* Let $X$ be a smooth complex projective variety. There are three main types of varieties.
−	* Not every variety is of one of these three types, but minimal model theory relates every variety to one of these extreme types
−	~~# Fano. This means that $−K_X$ is ample. (We recall the definition of ampleness in section 2.)~~
−	~~# Calabi-Yau. We define this to mean that $K_X$ is numerically trivial.~~
−	~~# ample canonical bundle. This means that $K_X$ is ample; it implies that $X$ is of general type.”~~
−	* Here, for $X$ of complex dimension $n$, the canonical bundle $K_X$ is the line bundle $\Omega^n_X$ of $n$-forms.
−	* We write $−K_X$ for the dual line bundle $K^∗_X$, the determinant of the tangent bundle.
−
−
−	~~==memo==~~
−	* http://mathoverflow.net/questions/120612/trichotomies-in-mathematics
−
−
−	~~==articles==~~
−	* Terragni, T. “Data about Hyperbolic Coxeter Systems.” arXiv:1503.08764 [math], March 30, 2015. http://arxiv.org/abs/1503.08764.
−	* Rastegar, Arash. ‘EPH-Classifications in Geometry, Algebra, Analysis and Arithmetic’. arXiv:1503.07859 [math], 26 March 2015. http://arxiv.org/abs/1503.07859.
−	* Totaro, Burt. ‘Algebraic Surfaces and Hyperbolic Geometry’. ArXiv E-Prints 1008 (1 August 2010): 3825.
−
−
−
−	~~[[분류:abstract concepts]]~~

@@ 21번째 줄: / 21번째 줄: @@
 ==articles==
 * Rastegar, Arash. ‘EPH-Classifications in Geometry, Algebra, Analysis and Arithmetic’. arXiv:1503.07859 [math], 26 March 2015. http://arxiv.org/abs/1503.07859.
 * Totaro, Burt. ‘Algebraic Surfaces and Hyperbolic Geometry’. ArXiv E-Prints 1008 (1 August 2010): 3825.

@@ 2번째 줄: / 2번째 줄: @@
 * spherical-Euclidean-hyperbolic
 * finite-affine-indefinite
-* {{수학노트|url=리만 사상 정리 Riemann mapping theorem and the uniformization theorem}}
+* {{수학노트|url=리만_사상_정리_Riemann_mapping_theorem_and_the_uniformization_theorem}}

← 이전 판	2020년 11월 16일 (월) 17:53 판
(차이 없음)

← 이전 판		2015년 3월 31일 (화) 00:52 판
2번째 줄:		2번째 줄:
	* spherical-Euclidean-hyperbolic		* spherical-Euclidean-hyperbolic
	* finite-affine-indefinite		* finite-affine-indefinite
		+	* {{수학노트\|url=리만 사상 정리 Riemann mapping theorem and the uniformization theorem}}

← 이전 판		2015년 3월 30일 (월) 06:13 판
1번째 줄:		1번째 줄:
		+	==introduction==
		+	* spherical-Euclidean-hyperbolic
		+	* finite-affine-indefinite
		+
		+	==articles==
	* Rastegar, Arash. ‘EPH-Classifications in Geometry, Algebra, Analysis and Arithmetic’. arXiv:1503.07859 [math], 26 March 2015. http://arxiv.org/abs/1503.07859.		* Rastegar, Arash. ‘EPH-Classifications in Geometry, Algebra, Analysis and Arithmetic’. arXiv:1503.07859 [math], 26 March 2015. http://arxiv.org/abs/1503.07859.


	[[분류:abstract concepts]]		[[분류:abstract concepts]]