Riemann Surfaces
نویسنده
چکیده
Riemann introduced his surfaces in the middle of the 19th century in order to “geometrize” complex analysis. In doing so, he paved the way for a great deal of modern mathematics such as algebraic geometry, manifold theory, and topology. So this would certainly be of interest to students in these areas, as well as in complex analysis or number theory. In simple terms, a Riemann surface is a surface which locally looks like the complex plane. We’ve all seen simple examples: open subsets of the plane, the sphere, and perhaps the domain of the “multivalued function” √ z. More exotic examples include elliptic curves, which includes what you get by identifying the sides of a square with corners 0, 1, i and 1 + i.
منابع مشابه
Pseudo-real Riemann surfaces and chiral regular maps
A Riemann surface is called pseudo-real if it admits anticonformal automorphisms but no anticonformal involution. Pseudo-real Riemann surfaces appear in a natural way in the study of the moduli space MKg of Riemann surfaces considered as Klein surfaces. The moduli space Mg of Riemann surfaces of genus g is a two-fold branched covering of MKg , and the preimage of the branched locus consists of ...
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