Plane algebraic curves : an introduction via valuations
著者
書誌事項
Plane algebraic curves : an introduction via valuations
（Monographs and textbooks in pure and applied mathematics, 61）
M. Dekker, c1981
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注記
Bibliography: p. 217-218
Includes index
内容説明・目次
内容説明
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.
目次
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
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