Links und Funktionen www. Hauptnavigation Math.
The Definition of Riemann Surfaces 2. Elementary Properties of Holomorphic Mappings 3.
Homotopy of Curves. The Fundamental Group 4.
Branched and Unbranched Coverings 5. The Universal Covering and Covering Transformations 6.
Sheaves 7. Analytic Continuation 8.
Algebraic Functions 9. Differential Forms The Integration of Differential Forms Cohomology Groups Dolbeault's Lemma A Finiteness Theorem The Exact Cohomology Sequence The Riemann-Roch Theorem Outlines and Lecture notes: Here is a tentative list of topics I plan to cover.
Problem of moduli. The Riemann-Hurwitz formula, the degree-genus formula. Field of mero- morphic functions, birational equivalence, connections with algebraic number theory.
Hyperbolic surfaces, Gauss-Bonnet theorem. The main theorem for compact Riemann surfaces and its consequences: The Riemann-Roch formula, the uniformization theorem, automorphisms of Riemann surfaces, Weierstrass points. Abelian varieties and abelian functions. Marking Policy It is also remarkable in its breath and scope and the clarity of exposition while keeping the required prerequisites to a bare mini- mum.
Here are some other good texts on the subject the list is by no means exhaustive : J. Bost,Introduction to compact Riemann surfaces, Jacobians, and abelian varieties, in From number theory to physics Les Houches, , Springer, Berlin. Forster, Lectures on Riemann surfaces.
This book grew out of lectures on Riemann surfaces which the author gave . In this section we define Riemann surfaces, holomorphic and meromorphic. This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an.
A very clear and lucid presen- tation. Farkas, I.
Kra, Riemann Surfaces. Jost, Compact Riemann Surfaces.
Reine Angew. Very close to the style of originals. The Necessity of Elliptic Functions for the Classification of Complex Tori Goals: - In the last few lectures, we have shown that the quotient of the upper half-plane by the unimodular group has a natural Riemann surface structure. That natural map was shown to be a covering map. We found this book important for the readers who want to know more about our old treasure so we brought it back to the shelves.
Kirwan, Complex Algebraic Curves. This one is more on the algebraic geometry side and at a more elementary level.