Complex algebraic curves

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This book introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.

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Title Statements

Full title :Complex algebraic curves / Frances Kirwan.

Summary

This book introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.

Edition Statements

Publication Date:1995, c1992.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge [England]
Language:eng
Publication Date:1995, c1992.

Notes

Description based upon print version of record.

The Physical Object

Description:1 online resource (274 p.).

Edition Identifiers

ISBN:1316086976, 9781316086971, 1107091314, 9781107091313, 1107088275, 9781107088276, 1107100305, 9781107100305, 1107094496, 9781107094499, 0511623925, 9780511623929
oclc:on1162248696
LC Classification:QA565
Dewey Decimal:516.3/52

Cover; Series Page; Title; Copyright; Contents; Preface; Chapter 1 Introduction and background; 1.1 A brief history of algebraic curves; 1.2 Relationship with other parts of mathematics; 1.2.1 Number theory; 1.2.2 Singularities and the theory of knots; 1.2.3 Complex analysis; 1.2.4 Abelian integrals; 1.3 Real Algebraic Curves; 1.3.1 Hilbert's Nullstellensatz; 1.3.2 Techniques for drawing real algebraic curves; 1.3.3 Real algebraic curves inside complex algebraic curves; 1.3.4 Important examples of real algebraic curves; Chapter 2 Foundations; 2.1 Complex algebraic curves in C2

2.2 Complex projective spaces2.3 Complex projective curves in P2; 2.4 Affine and projective curves; 2.5 Exercises; Chapter 3 Algebraic properties; 3.1 Bezout's theorem; 3.2 Points of inflection and cubic curves; 3.3 Exercises; Chapter 4 Topological properties; 4.1 The degree-genus formula; 4.1.1 The first method of proof; 4.1.2 The second method of proof; 4.2 Branched covers of PI; 4.3 Proof of the degree-genus formula; 4.4 Exercises; Chapter 5 Riemann surfaces; 5.1 The Weierstrass p-function; 5.2 Riemann surfaces; 5.3 Exercises; Chapter 6 Differentials on Riemann surfaces

6.1 Holomorphic differentials6.2 …