Symmetries of Compact Riemann Surfaces (Paperback, 2010 ed.)

The content of this monograph is situated in the intersection of important branches of mathematics like the theory of one complex variable, algebraic geometry, low dimensional topology and, from the point of view of the techniques used, com- natorial group theory. The main tool comes from the Uniformization Theorem for Riemannsurfaces, whichrelatesthetopologyofRiemannsurfacesandholomorphic or antiholomorphic actions on them to the algebra of classical cocompact Fuchsian groups or, more generally, non-euclidean crystallographic groups. Foundations of this relationship were established by A. M. Macbeath in the early sixties and dev- oped later by, among others, D. Singerman. Another important result in Riemann surface theory is the connection between Riemannsurfacesandtheir symmetrieswith complexalgebraiccurvesandtheirreal forms. Namely, there is a well known functorial bijective correspondence between compact Riemann surfaces and smooth, irreducible complex projective curves. The fact that a Riemann surface has a symmetry means, under this equivalence, that the corresponding complex algebraic curve has a real form, that is, it is the complex- cation of a real algebraic curve. Moreover, symmetries which are non-conjugate in the full group of automorphisms of the Riemann surface, correspond to real forms which are birationally non-isomorphic over the reals. Furthermore, the set of points xedbyasymmetryishomeomorphictoaprojectivesmoothmodeloftherealform

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Lecture Notes in Mathematics, 2007
Release date:	October 2010
First published:	2010
Authors:	Emilio Bujalance • Francisco Javier Cirre • Jose Manuel Gamboa • Grzegorz Gromadzki
Dimensions:	235 x 155 x 10mm (L x W x T)
Format:	Paperback
Pages:	164
Edition:	2010 ed.
ISBN-13:	978-3-642-14827-9
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Books > Science & Mathematics > Mathematics > Topology > General
LSN:	3-642-14827-1
Barcode:	9783642148279

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