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Algebraic Curves, the Brill and Noether Way

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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.

Author(s): Eduardo Casas Alvero
Series: Universitext
Edition: 1
Publisher: Springer
Year: 2019

Language: English
Pages: 237
Tags: Algebraic Curves

Front Matter ....Pages i-xiv
Hypersurfaces, Elementary Facts (Eduardo Casas-Alvero)....Pages 1-26
Local Properties of Plane Curves (Eduardo Casas-Alvero)....Pages 27-56
Projective Properties of Plane Curves (Eduardo Casas-Alvero)....Pages 57-108
The Intrinsic Geometry on a Curve (Eduardo Casas-Alvero)....Pages 109-216
Back Matter ....Pages 217-224