The book presents the central facts of the local, projective and intrinsic theories of complex algebraic plane curves, with complete proofs and starting from low-level prerequisites. It includes Puiseux series, branches, intersection multiplicity, Bézout theorem, rational functions, Riemann-Roch theorem and rational maps. It is aimed at graduate and advanced undergraduate students, and also at anyone interested in algebraic curves or in an introduction to algebraic geometry via curves.

Autorentext

Eduardo Casas Alvero is Emeritus Professor at the University of Barcelona since October 2018, where he has been since the early seventies. His main research interests are in algebraic geometry. Casas Alvero is the author of numerous publications including several other successful books, including the following: Analytic Projective Geometry (EMS Publishing House, 2014), Singularities of Plane Curves (London Mathematical Society Lecture Notes Series 279, Cambridge University Press 2000) and Enumerative Theory of conics after Halphen (Lecture Notes in Mathematics 1196, Springer 1986).

Inhalt

1. Hypersurfaces, elementary facts. -2. Local properties of plane curves. -3. Projective properties of plane curves. - 4. The intrinsic geometry of a curve