"Belyi map"의 두 판 사이의 차이
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==introduction== | ==introduction== | ||
| − | * Belyi's theorem on algebraic curves | + | * Belyi's theorem on algebraic curves |
| − | ** any non-singular algebraic curve C, defined by algebraic number coefficients, represents a compact Riemann surface which is a ramified covering of the Riemann sphere, ramified at three points only. | + | ** any non-singular algebraic curve C, defined by algebraic number coefficients, represents a compact Riemann surface which is a ramified covering of the Riemann sphere, ramified at three points <math>\{0,1,\infty\}</math> only. |
* Belyi map gives rise to a projective curve | * Belyi map gives rise to a projective curve | ||
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==Belyi maps of degree 2== | ==Belyi maps of degree 2== | ||
| − | * Belyi map f:\mathbb{P}^1\to \mathbb{P}^1 defined by z\mapsto z^2 | + | * Belyi map <math>f:\mathbb{P}^1\to \mathbb{P}^1</math> defined by <math>z\mapsto z^2</math> |
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==Grobner techniques== | ==Grobner techniques== | ||
| − | * start with three permutations (12), (23), (132). They generate S_3. | + | * start with three permutations <math>(12), (23), (132)</math>. They generate <math>S_3</math>. |
| − | * Riemann-Hurwitz formula gives the genus g=1-3+(1+1+2)/2=0 | + | * Riemann-Hurwitz formula gives the genus <math>g=1-3+(1+1+2)/2=0</math> |
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==complex analytic method== | ==complex analytic method== | ||
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* using modular forms | * using modular forms | ||
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==p-adic method== | ==p-adic method== | ||
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==related items== | ==related items== | ||
| − | + | * [[Dessin d'enfant]] | |
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==expositions== | ==expositions== | ||
| + | * Sijsling, Jeroen, and John Voight. 2013. “On Computing Belyi Maps.” arXiv:1311.2529 [math] (November 11). http://arxiv.org/abs/1311.2529. | ||
| + | * Zvonkin, [https://www.labri.fr/perso/zvonkin/Research/belyi.pdf Belyi functions: examples, properties, and applications] | ||
| + | * Magot, Nicolas, and Alexander Zvonkin. 2000. “Belyi Functions for Archimedean Solids.” Discrete Mathematics 217 (1–3) (April 28): 249–271. doi:10.1016/S0012-365X(99)00266-6. | ||
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==articles== | ==articles== | ||
| + | * Ayberk Zeytin, Belyi Lattes Maps, arXiv:1011.5644[math.AG], November 25 2010, http://arxiv.org/abs/1011.5644v3 | ||
| + | * Van Hoeij, Mark, and Raimundas Vidunas. “Belyi Functions for Hyperbolic Hypergeometric-to-Heun Transformations.” Physical Review Letters 111, no. 10 (September 2013). doi:10.1103/PhysRevLett.111.107802. | ||
| + | * Klug, Michael, Michael Musty, Sam Schiavone, and John Voight. 2013. “Numerical Calculation of Three-Point Branched Covers of the Projective Line.” arXiv:1311.2081 [math] (November 8). http://arxiv.org/abs/1311.2081. | ||
| + | * Köck, Bernhard. “Belyi’s Theorem Revisited.” arXiv:math/0108222, August 31, 2001. http://arxiv.org/abs/math/0108222. | ||
| − | + | ==encyclopedia== | |
| − | * http:/ | + | * http://en.wikipedia.org/wiki/Dessin_d%27enfant |
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| − | + | [[분류:개인노트]] | |
| + | [[분류:math and physics]] | ||
| + | [[분류:math]] | ||
| + | [[분류:migrate]] | ||
| − | + | ==메타데이터== | |
| − | + | ===위키데이터=== | |
| − | + | * ID : [https://www.wikidata.org/wiki/Q3024615 Q3024615] | |
| − | + | ===Spacy 패턴 목록=== | |
| − | + | * [{'LOWER': 'dessin'}, {'LEMMA': "d'enfant"}] | |
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2021년 2월 17일 (수) 03:14 기준 최신판
introduction
- Belyi's theorem on algebraic curves
- any non-singular algebraic curve C, defined by algebraic number coefficients, represents a compact Riemann surface which is a ramified covering of the Riemann sphere, ramified at three points \(\{0,1,\infty\}\) only.
- Belyi map gives rise to a projective curve
Belyi maps of degree 2
- Belyi map \(f:\mathbb{P}^1\to \mathbb{P}^1\) defined by \(z\mapsto z^2\)
Grobner techniques
- start with three permutations \((12), (23), (132)\). They generate \(S_3\).
- Riemann-Hurwitz formula gives the genus \(g=1-3+(1+1+2)/2=0\)
complex analytic method
- using modular forms
p-adic method
expositions
- Sijsling, Jeroen, and John Voight. 2013. “On Computing Belyi Maps.” arXiv:1311.2529 [math] (November 11). http://arxiv.org/abs/1311.2529.
- Zvonkin, Belyi functions: examples, properties, and applications
- Magot, Nicolas, and Alexander Zvonkin. 2000. “Belyi Functions for Archimedean Solids.” Discrete Mathematics 217 (1–3) (April 28): 249–271. doi:10.1016/S0012-365X(99)00266-6.
articles
- Ayberk Zeytin, Belyi Lattes Maps, arXiv:1011.5644[math.AG], November 25 2010, http://arxiv.org/abs/1011.5644v3
- Van Hoeij, Mark, and Raimundas Vidunas. “Belyi Functions for Hyperbolic Hypergeometric-to-Heun Transformations.” Physical Review Letters 111, no. 10 (September 2013). doi:10.1103/PhysRevLett.111.107802.
- Klug, Michael, Michael Musty, Sam Schiavone, and John Voight. 2013. “Numerical Calculation of Three-Point Branched Covers of the Projective Line.” arXiv:1311.2081 [math] (November 8). http://arxiv.org/abs/1311.2081.
- Köck, Bernhard. “Belyi’s Theorem Revisited.” arXiv:math/0108222, August 31, 2001. http://arxiv.org/abs/math/0108222.
encyclopedia
메타데이터
위키데이터
- ID : Q3024615
Spacy 패턴 목록
- [{'LOWER': 'dessin'}, {'LEMMA': "d'enfant"}]