Symmetries of Compact Riemann Surfaces

*- Paperback*

2010, ISBN: 3642148271

[EAN: 9783642148279], Neubuch, [PU: Springer-Verlag Gmbh Okt 2010], ALGEBRAISCHE GEOMETRIE; GEOMETRIE / DIFFERENZIALTOPOLOGIE ( TOPOLOGIE ); -, Neuware - 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. 158 pp. Englisch

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*- Paperback*

2010, ISBN: 9783642148279

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. Buch (fremdspr.) Emilio Bujalance#Francisco Javier Cirre#José Manuel Gamboa#Grzegorz Gromadzki Taschenbuch, Springer Berlin, 06.10.2010, Springer Berlin, 2010

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Symmetries of Compact Riemann Surfaces (Lecture Notes in Mathematics)

*- new book*

ISBN: 9783642148279

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.; Science & Nature, Springer

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Symmetries of Compact Riemann Surfaces

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Symmetries of Compact Riemann Surfaces

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2010, ISBN: 9783642148279

2010, Softcover, Buch, [PU: Springer Berlin]

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# Symmetries of Compact Riemann Surfaces* - Paperback*

2010, ISBN: 3642148271

[EAN: 9783642148279], Neubuch, [PU: Springer-Verlag Gmbh Okt 2010], ALGEBRAISCHE GEOMETRIE; GEOMETRIE / DIFFERENZIALTOPOLOGIE ( TOPOLOGIE ); -, Neuware - The content of this monograph is … More...

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Symmetries of Compact Riemann Surfaces (Lecture Notes in Mathematics)

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## ISBN: 9783642148279

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 an… More...

No. 9783642148279. Shipping costs:20, (EUR 3.34)

Symmetries of Compact Riemann Surfaces

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2010, ISBN: 9783642148279

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Symmetries of Compact Riemann Surfaces

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2010, ISBN: 9783642148279

2010, Softcover, Buch, [PU: Springer Berlin]

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** Details of the book - Symmetries of Compact Riemann Surfaces**

EAN (ISBN-13): 9783642148279

ISBN (ISBN-10): 3642148271

Hardcover

Paperback

Publishing year: 2010

Publisher: Springer Berlin

158 Pages

Weight: 0,284 kg

Language: eng/Englisch

Book in our database since 2009-06-13T07:16:10-04:00 (New York)

Detail page last modified on 2020-09-03T14:37:21-04:00 (New York)

ISBN/EAN: 3642148271

ISBN - alternate spelling:

3-642-14827-1, 978-3-642-14827-9

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