Courbes algébriques planes. (Plane algebraic curves). (French) Zbl 0557.14016

Publications Mathématiques de l’Université Paris VII, 4. Paris: Université de Paris VII, U.E.R. de Mathématiques. 203 p. (1978).
From the introduction: ”The idea of the course on which this textbook is based was to examine a particular problem (the Bezout theorem of curves) and to introduce certain tools for the global and local study of a curve (for example: projective notions, Weierstrass preparation theorem, Puiseux theorem, places, etc.). The only original features are the figures in chapter IV (where we ”see” that \(X^ 3+Y^ 3+Z^ 3=0\) is a torus) and the passage from formal Puiseux series to convergent Puiseux series (where the blowings-up occur naturally)”. Contents: 0. Algebraic subsets of \({\mathbb{C}}^ n\); I. Affine algebraic sets; II. Affine plane curves; III. Projective algebraic sets; IV. Plane projective curves: the Bezout theorem; V. The resultant; VI. Local point of view: rings of formal power series; VII. Rings of convergent series; VIII. The Puiseux theorem; IX. Local theory of intersection of curves; Appendix: A rationality criterion for formal power series.


14H20 Singularities of curves, local rings
14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
14Hxx Curves in algebraic geometry