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Monthly Archives: September 2013
Lecture 15: Monday, September 23, 2013
Today we discuss how some familiar objects — namely the circle, the sphere, the torus, and even elliptic curves — are each examples of non-singular algebraic curves which are also compact, connected Riemann surfaces. Advertisements
Lecture 14: Friday, September 20, 2013
Eventually, we wish to show that every compact, connected Riemann surface is a nonsingular algebraic curve. Today, we discuss what is means to be a “nonsingular algebraic curve” using Dedekind Domains.
Posted in MA 59800
Tagged Algebraic Curve, Algebraic Variety, Coordinate ring, Dedekind domain, Discrete Valuation, Discrete Valuation Ring, Integral domain, Jacobian matrix, Localization, Maximal ideal, Oscar Zariski, Polynomial ring, Prime ideal, Principal Ideal, Radical of an Ideal, Tangent space, Zariski cotangent space
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“An Elementary Approach to Dessins d’enfants and the Grothendieck-Teichmüller Group” by Pierre Guillot
Pierre Guillot has a new paper on the ArXiv entitled “An Elementary Approach to Dessins d’enfants and the Grothendieck-Teichmüller Group”.
“Hecke Groups, Dessins d’Enfants and the Archimedean Solids” by Yang-Hui He and James Read
Yang-Hui He and James Read have a new paper on the ArXiv entitled “Hecke Groups, Dessins d’Enfants and the Archimedean Solids”.
“Regular Dessins with a Given Automorphism Group” by Gareth A. Jones
Gareth A. Jones has a new paper on the ArXiv entitled “Regular Dessins with a Given Automorphism Group”.
Lecture 13: Wednesday, September 18, 2013
In Lecture 11 and Lecture 12, we discussed examples of Riemann Surfaces and their relation with the Riemann Sphere . Today, we put things into perspective by considering the larger picture: we discuss tesselations of the upper half plane, covering … Continue reading
Lecture 12: Monday, September 16, 2013
Last time, we introduced the Fundamental Domain in terms of the extended complex plane . Felix Klein showed the existence of a function , invariant under , giving these isomorphisms. Today, we use Richard Dedekind‘s function to create similar functions … Continue reading
