"Elliptic-Parabolic-Hyperbolic trichotomy in mathematics"의 두 판 사이의 차이
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* spherical-Euclidean-hyperbolic | * spherical-Euclidean-hyperbolic | ||
* finite-affine-indefinite | * finite-affine-indefinite | ||
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| + | ==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. | ||
| 10번째 줄: | 20번째 줄: | ||
==articles== | ==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. | ||
| + | * Totaro, Burt. ‘Algebraic Surfaces and Hyperbolic Geometry’. ArXiv E-Prints 1008 (1 August 2010): 3825. | ||
| + | |||
[[분류:abstract concepts]] | [[분류:abstract concepts]] | ||
2015년 3월 30일 (월) 16:52 판
introduction
- spherical-Euclidean-hyperbolic
- finite-affine-indefinite
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
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.