Complex Algebraic Curves

Name: Complex Algebraic Curves
Price: 55.43 USD
Availability: InStock
ISBN: 9780521423533

ISBN-10: 0521423538

ISBN-13: 9780521423533

Edition: 1992

Authors: Frances Kirwan, C. M. Series, J. W. Bruce

List price: $70.99

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Description:

Complex algebraic curves were developed in the nineteenth century. They have many fascinating properties and crop up in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired by most undergraduate courses in mathematics, Dr Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis. This book grew from a lecture course given by Dr Kirwan at Oxford University and will be an excellent companion for final year undergraduates and graduates who are studying complex algebraic curves.

Book details

List price: $70.99
Copyright year: 1992
Publisher: Cambridge University Press
Publication date: 2/20/1992
Binding: Paperback
Pages: 276
Size: 6.02" wide x 9.02" long x 0.71" tall
Weight: 0.748
Language: English




Introduction and background



A brief history of algebraic curves



Relationship with other parts of mathematics



Number theory



Singularities and the theory of knots



Complex analysis



Abelian integrals



Real Algebraic Curves



Hilbert's Nullstellensatz



Techniques for drawing real algebraic curves



Real algebraic curves inside complex algebraic curves



Important examples of real algebraic curves



Foundations



Complex algebraic curves in C[superscript 2]



Complex projective spaces



Complex projective curves in P[subscript 2]



Affine and projective curves



Exercises



Algebraic properties



Bezout's theorem



Points of inflection and cubic curves



Exercises



Topological properties



The degree-genus formula



The first method of proof



The second method of proof



Branched covers of P[subscript 1]



Proof of the degree-genus formula



Exercises



Riemann surfaces



The Weierstrass [weierp]-function



Riemann surfaces



Exercises



Differentials on Riemann surfaces



Holomorphic differentials



Abel's theorem



The Riemann-Roch theorem



Exercises



Singular curves



Resolution of singularities



Newton polygons and Puiseux expansions



The topology of singular curves



Exercises



Algebra



Complex analysis



Topology



Covering projections



The genus is a topological invariant



Spheres with handles