Topics in the Theory of Riemann Surfaces

Focusing on the automorphisms of Riemann surfaces, this monograph gives a foundational treatment from the point of view of Galois coverings, and treats 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. The text is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.