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Symmetries of Compact Riemann Surfaces
Contributor(s): Bujalance, Emilio, Cirre, Francisco Javier, Gamboa, Jose Manuel, Grodmadzki, Grzegorz
ISBN: 3642148271     ISBN-13: 9783642148279
Publisher: Springer Verlag
    OUR PRICE: $49.95  
Product Type: Paperback - Other Formats
Published: October 2010
Annotation: 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.
Additional Information
BISAC Categories:
- Mathematics | Mathematical Analysis
- Mathematics | Geometry | Algebraic
- Mathematics | Algebra | Abstract
Dewey: 515
Academic/Grade Level: Scholarly/Graduate
Series: Lecture Notes in Mathematics
Book type: Non-Fiction
Physical Information: 9.50" H x 6.25" W x 0.50" (0.62 lbs) 158 pages