"Elliptic-Parabolic-Hyperbolic trichotomy in mathematics"의 두 판 사이의 차이

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-==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]]

"Elliptic-Parabolic-Hyperbolic trichotomy in mathematics"의 두 판 사이의 차이

2020년 11월 13일 (금) 07:53 판

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