Bibliographic Information

Symmetries of compact Riemann surfaces

Emilio Bujalance ... [et al.]

(Lecture notes in mathematics, 2007)

Springer, c2010

Available at  / 51 libraries

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Note

Other authors: Francisco Javier Cirre, José Manuel Gamboa, Grzegorz Gromadzki

Includes bibliographical references (p. 151-155) and index

Description and Table of Contents

Description

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.

Table of Contents

Preliminaries.- On the Number of Conjugacy Classes of Symmetries of Riemann Surfaces.- Counting Ovals of Symmetries of Riemann Surfaces.- Symmetry Types of Some Families of Riemann Surfaces.- Symmetry Types of Riemann Surfaces with a Large Group of Automorphisms.

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Details

  • NCID
    BB03813210
  • ISBN
    • 9783642148279
  • LCCN
    2010935187
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Berlin
  • Pages/Volumes
    xx, 158 p.
  • Size
    24 cm
  • Classification
  • Parent Bibliography ID
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