"Belyi map"의 두 판 사이의 차이
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encyclopedia==
imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
imported>Pythagoras0 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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| 1번째 줄: | 1번째 줄: | ||
| − | ==introduction | + | ==introduction== |
* Belyi's theorem on algebraic curves<br> | * Belyi's theorem on algebraic curves<br> | ||
| 9번째 줄: | 9번째 줄: | ||
| − | ==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 f:\mathbb{P}^1\to \mathbb{P}^1 defined by z\mapsto z^2 | ||
| 17번째 줄: | 17번째 줄: | ||
| − | ==Grobner techniques | + | ==Grobner techniques== |
* start with three permutations (12), (23), (132). They generate S_3. | * start with three permutations (12), (23), (132). They generate S_3. | ||
| 26번째 줄: | 26번째 줄: | ||
| − | ==complex analytic method | + | ==complex analytic method== |
* using modular forms | * using modular forms | ||
| 34번째 줄: | 34번째 줄: | ||
| − | ==p-adic method | + | ==p-adic method== |
| 44번째 줄: | 44번째 줄: | ||
| − | ==history | + | ==history== |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
| 52번째 줄: | 52번째 줄: | ||
| − | ==related items | + | ==related items== |
| 58번째 줄: | 58번째 줄: | ||
| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia== |
* http://en.wikipedia.org/wiki/Dessin_d%27enfant | * http://en.wikipedia.org/wiki/Dessin_d%27enfant | ||
| 70번째 줄: | 70번째 줄: | ||
| − | ==books | + | ==books== |
| 82번째 줄: | 82번째 줄: | ||
| − | ==expositions | + | ==expositions== |
| 88번째 줄: | 88번째 줄: | ||
| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles== |
| 104번째 줄: | 104번째 줄: | ||
| − | ==question and answers(Math Overflow) | + | ==question and answers(Math Overflow)== |
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
| 116번째 줄: | 116번째 줄: | ||
| − | ==blogs | + | ==blogs== |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
| 127번째 줄: | 127번째 줄: | ||
| − | ==experts on the field | + | ==experts on the field== |
* [http://www.cems.uvm.edu/%7Evoight/ http://www.cems.uvm.edu/~voight/] | * [http://www.cems.uvm.edu/%7Evoight/ http://www.cems.uvm.edu/~voight/] | ||
| 136번째 줄: | 136번째 줄: | ||
| − | ==links | + | ==links== |
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내] | * [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내] | ||
2012년 10월 28일 (일) 14:22 판
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 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
history
encyclopedia==
- http://en.wikipedia.org/wiki/Dessin_d%27enfant
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
expositions
articles==
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://math.stackexchange.com/search?q=
- http://physics.stackexchange.com/search?q=
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field
links
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://math.stackexchange.com/search?q=
- http://physics.stackexchange.com/search?q=
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field