Robert D. M. Accola (auth.)3540587217, 9783540587217, 0387587217
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. |
Table of contents :
Review of some basic concepts in the theory of Riemann surfaces….Pages 1-12
Some exceptional points on Riemann surfaces….Pages 13-19
The inequality of Castelnuovo-Severi….Pages 20-29
Smooth and branched coverings of Riemann surfaces….Pages 30-41
Automorphisms of Riemann surfaces, I….Pages 42-51
When are fixed points of automorphisms exceptional in some other sense?….Pages 52-73
Automorphisms of Riemann surfaces, II; N(p)….Pages 74-98 |
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