Overview

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 HomologyCellular HomologyDe Rham Cohomology Commutative Algebra — An Introduction — Closed Ideals and VarietiesCoordinate RingsDimension TheoryIntersection Numbers Singular Plane Curves — The Classical Plücker Formulae Divisors on a Compact Complex Manifold — Divisors and Holomorphic Line BundlesLinear Systems on a Compact Riemann Surface and Holomorphic Maps Compact Riemann Surfaces — The Jacobian Variety and Abel's TheoremThe Riemann-Roch Theorem and the Canonical EmbeddingHyperelliptic Riemann Surfaces and the Weierstrass PointsGeometry of Projective Curves — The Complex Flag ManifoldMetric Geometry of Projective CurvesPlücker Formulae for Projective Algebraic CurvesHarmonic Maps from a Compact Riemann Surface A Brief Look at Algebraic Surfaces — The Intersection FormBlow-Ups and Rational MapsThe Kodaira Dimension of an Algebraic SurfaceReadership: Mathematicians.

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9781299462540

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