"Belyi map"의 두 판 사이의 차이
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| 19번째 줄: | 19번째 줄: | ||
<h5>Grobner techniques</h5> | <h5>Grobner techniques</h5> | ||
| − | * | + | * 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 | ||
| 27번째 줄: | 28번째 줄: | ||
<h5>complex analytic method</h5> | <h5>complex analytic method</h5> | ||
| − | + | * using modular forms | |
| 128번째 줄: | 129번째 줄: | ||
<h5>experts on the field</h5> | <h5>experts on the field</h5> | ||
| + | * [http://www.cems.uvm.edu/%7Evoight/ http://www.cems.uvm.edu/~voight/] | ||
* http://arxiv.org/ | * http://arxiv.org/ | ||
2012년 3월 8일 (목) 08:59 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