Plane Algebraic Curves
1st Edition
Published on 11. December 2024
240 pages
978-1-040-28002-7 (ISBN)
Description
This book introduces the contemporary notions of algebraic varieties, morphisms of varieties, and adeles to the classical subject of plane curves over algebraically closed fields. It is useful for advanced undergraduate and beginning graduate students in mathematics.
More details
Series
Edition
1. Auflage
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Professional and scholarly
ISBN-13
978-1-040-28002-7 (9781040280027)
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Schweitzer Classification
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Additional editions
Content
1. Prerequisites 2. Some Facts About Polynomials 3. Affine Plane Curves 4. Tangent Spaces 5. The Local Ring at a Point 6. Projective Plane Curves 7. Rational Mappings, Birational Correspondences and Isomorphisms of Curves 8. Examples of Rational Curves 9. The Correspondence between Valuations and Points 10. An Overview and Sideways Glance 11. Divisors 12. The Divisor of a Function Has Degree 13. Riemann's Theorem 14. The Genus of a Nonsingular Plane Curve 15. Curves of Genus 0 and 1 16. A Classification of Isomorphism Classes of Curves of Genus 1 17. The Genus of a Singular Curve 18. Inflection Points on Plane Curves 19. Bezout's Theorem 20. Addition on a Nonsingular Cubic 21. Derivations, Differentials and the Canonical Class 22. Adeles and the Riemann-Roch Theorem
