Notes on Compact Riemann Surfaces
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چکیده
منابع مشابه
Introduction to Compact Riemann Surfaces
The theory of Riemann surfaces is a classical field of mathematics where geometry and analysis play equally important roles. The purpose of these notes is to present some basic facts of this theory to make this book more self contained. In particular we will deal with classical descriptions of Riemann surfaces, Abelian differentials, periods on Riemann surfaces, meromorphic functions, theta fun...
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These are some notes that I collected from my readings about Riemann surfaces. Most of the notes are based on Beardon’s book Primer on Riemann Surfaces. These notes will serve as my lecture notes for a 25 minute talk I am giving in my Algebraic Topology class. I was not able to cover the last section during the talk.
متن کاملIsometry Groups of Compact Riemann Surfaces
We explore the structure of compact Riemann surfaces by studying their isometry groups. First we give two constructions due to Accola [1] showing that for all g ≥ 2, there are Riemann surfaces of genus g that admit isometry groups of at least some minimal size. Then we prove a theorem of Hurwitz giving an upper bound on the size of any isometry group acting on any Riemann surface of genus g ≥ 2...
متن کاملCompact Riemann Surfaces: a Threefold Categorical Equivalence
We define and prove basic properties of Riemann surfaces, which we follow with a discussion of divisors and an elementary proof of the RiemannRoch theorem for compact Riemann surfaces. The Riemann-Roch theorem is used to prove the existence of a holomorphic embedding from any compact Riemann surface into n-dimensional complex projective space Pn. Using comparison principles such as Chow’s theor...
متن کاملA Poincaré-bendixson Theorem for Meromorphic Connections on Riemann Surfaces
We shall prove a Poincaré-Bendixson theorem describing the asymptotic behavior of geodesics for a meromorphic connection on a compact Riemann surface. We shall also briefly discuss the case of non-compact Riemann surfaces, and study in detail the geodesics for a holomorphic connection on a complex torus.
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تاریخ انتشار 2009