Belyi map

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

 

 

 

 

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

 

 

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

 

• 2011년 books and articles
• http://library.nu/search?q=
• http://library.nu/search?q=

 

 

 

 

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://blogsearch.google.com/blogsearch?q=
    
  • http://blogsearch.google.com/blogsearch?q=
• http://ncatlab.org/nlab/show/HomePage

 

 

experts on the field

• http://www.cems.uvm.edu/~voight/
• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내