Topics in the Theory of Riemann Surfaces
Accola, Robert D. M.
Topics in the Theory of Riemann Surfaces [electronic resource] / by Robert D. M. Accola. - X, 110 p. online resource. - Lecture Notes in Mathematics, 1595 0075-8434 ; . - Lecture Notes in Mathematics, 1595 .
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).
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.
9783540490562
10.1007/BFb0073575 doi
Geometry, algebraic.
Group theory.
Algebraic Geometry.
Group Theory and Generalizations.
QA564-609
516.35
Topics in the Theory of Riemann Surfaces [electronic resource] / by Robert D. M. Accola. - X, 110 p. online resource. - Lecture Notes in Mathematics, 1595 0075-8434 ; . - Lecture Notes in Mathematics, 1595 .
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).
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.
9783540490562
10.1007/BFb0073575 doi
Geometry, algebraic.
Group theory.
Algebraic Geometry.
Group Theory and Generalizations.
QA564-609
516.35