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© 2016

What is the Genus?

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2162)

Also part of the History of Mathematics Subseries book sub series (HISTORYMS, volume 2162)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Algebraic Curves

    1. Front Matter
      Pages 3-3
    2. Patrick Popescu-Pampu
      Pages 5-6
    3. Patrick Popescu-Pampu
      Pages 7-8
    4. Patrick Popescu-Pampu
      Pages 9-10
    5. Patrick Popescu-Pampu
      Pages 11-13
    6. Patrick Popescu-Pampu
      Pages 15-16
    7. Patrick Popescu-Pampu
      Pages 17-18
    8. Patrick Popescu-Pampu
      Pages 19-20
    9. Patrick Popescu-Pampu
      Pages 21-22
    10. Patrick Popescu-Pampu
      Pages 23-24
    11. Patrick Popescu-Pampu
      Pages 25-26
    12. Patrick Popescu-Pampu
      Pages 27-30
    13. Patrick Popescu-Pampu
      Pages 31-33
    14. Patrick Popescu-Pampu
      Pages 35-40
    15. Patrick Popescu-Pampu
      Pages 41-42
    16. Patrick Popescu-Pampu
      Pages 43-44
    17. Patrick Popescu-Pampu
      Pages 45-49
    18. Patrick Popescu-Pampu
      Pages 51-52

About this book

Introduction

Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena.

Keywords

01A05, 14-03, 30-03, 55-03 Genus Riemann surfaces Algebraic varieties Homology Riemann-Roch theorem

Authors and affiliations

  1. 1.UFR de MathématiquesUniversitè Lille 1Villeneuve d’AscqFrance

Bibliographic information

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Reviews

“This book provides a fascinating—yet technically quite demanding—tour of the ideas and generalizations that feed into our modern conception of the genus. It should therefore serve as a useful starting point for historical and even philosophical investigations into past mathematical practice of forming and shaping concepts. It may also be useful in teaching advanced mathematical content with a view to historical development … .” (Henrik Kragh Sørensen, ISIS, Vol. 109 (2), June, 2018)

“This book is addressed to any person with a little knowledge of mathematics (such as an undergraduate student) who wants to get an idea of some of the most important concepts that arose in geometry and topology in the last couple of centuries: the author has made a commendable effort to explain all the more advanced concepts almost from scratch (but obviously this was not possible for the last chapter).” (Pietro De Poi, Mathematical Reviews, July, 2017)

“This clear book thoroughly covers the metamorphosis and theoretical significance of the genus by using several historical approaches that incorporate discussions related to analysis, algebraic geometry, number theory, and topology. … The book contains 20 figures and concludes with a list of 200 references and an index, which will help those who wish to delve into deeper studies. Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals.” (D. P. Turner, Choice, Vol. 54 (9), May, 2017)