System Upgrade on Tue, May 28th, 2024 at 2am (EDT)
Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.
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.
