Topics in the Theory of Riemann Surfaces

1994
ISBN: 978-3-540-58721-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1595, 110 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 195 g

Reihe: Lecture Notes in Mathematics

The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.

Zielgruppe

Research

Autoren/Hrsg.

Accola, Robert D. M.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Review of some basic concepts in the theory of Riemann surfaces.- Some exceptional points on Riemann surfaces.- The inequality of Castelnuovo-Severi.- Smooth and branched coverings of Riemann surfaces.- Automorphisms of Riemann surfaces, I.- When are fixed points of automorphisms exceptional in some other sense?.- Automorphisms of Riemann surfaces, II; N(p).