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Algebraic Curves, the Brill and Noether Way

  • Textbook
  • © 2019

Overview

Authors:
  1. Eduardo Casas-Alvero

    1. Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, Spain

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  • Complete, self-contained presentation with proofs
  • Low-level prerequisites
  • Matter is presented from a decidedly geometric viewpoint, updating classical approaches
  • Exercises at the end of each chapter

Part of the book series: Universitext (UTX)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Hypersurfaces, Elementary Facts

    • Eduardo Casas-Alvero
    Pages 1-26

  3. Local Properties of Plane Curves

    • Eduardo Casas-Alvero
    Pages 27-56

  4. Projective Properties of Plane Curves

    • Eduardo Casas-Alvero
    Pages 57-108

  5. The Intrinsic Geometry on a Curve

    • Eduardo Casas-Alvero
    Pages 109-216

  6. Back Matter

    Pages 217-224
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Keywords

About this book

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.

 

Reviews

“The author … produces a detailed, gradual introduction into the topic, which is not only extremely effective, but also highly enjoyable for its simple, fluent writing style.” (Margherita Barile, Mathematical Reviews, October, 2020)

Authors and Affiliations

  • Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, Spain

    Eduardo Casas-Alvero

About the author

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).

Bibliographic Information

  • Book Title: Algebraic Curves, the Brill and Noether Way

  • Authors: Eduardo Casas-Alvero

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-030-29016-0

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Softcover ISBN: 978-3-030-29015-3Published: 05 December 2019

  • eBook ISBN: 978-3-030-29016-0Published: 30 November 2019

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XIV, 224

  • Topics: Algebraic Geometry

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