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Series in Pure Mathematics - Vol. 10
COMPACT RIEMANN SURFACES AND ALGEBRAIC CURVES
by Kichoon Yang (Arkansas State Univ.)
This volume is an introduction to the theory of Compact Riemann Surfaces and algebraic curves. It gives a concise account of the elementary aspects of different viewpoints in curve theory. Foundational results on divisors and compact Riemann surfaces are also stated and proved.
Contents:
- Topological Preliminaries — Singular
Homology and Relative Homology
- Cellular Homology
- De Rham Cohomology
- Commutative Algebra — An Introduction — Closed Ideals and Varieties
- Coordinate Rings
- Dimension Theory
- Intersection Numbers
- Singular Plane Curves — The Classical Plücker Formulae
- Divisors on a Compact Complex Manifold — Divisors and Holomorphic Line Bundles
- Linear Systems on a Compact Riemann Surface and Holomorphic Maps
- Compact Riemann Surfaces — The Jacobian Variety and Abel's Theorem
- The Riemann-Roch Theorem and the Canonical Embedding
- Hyperelliptic Riemann Surfaces and the Weierstrass Points
- Geometry of Projective Curves — The Complex Flag Manifold
- Metric Geometry of Projective Curves
- Plücker Formulae for Projective Algebraic Curves
- Harmonic Maps from a Compact Riemann Surface
- A Brief Look at Algebraic Surfaces — The Intersection Form
- Blow-Ups and Rational Maps
- The Kodaira Dimension of an Algebraic Surface
Readership: Mathematicians.
| 184pp |
Pub. date: Nov 1988 |
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