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What is the Genus?

  • Patrick Popescu-Pampu

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
    19. Patrick Popescu-Pampu
      Pages 53-57
    20. Patrick Popescu-Pampu
      Pages 59-61
    21. Patrick Popescu-Pampu
      Pages 63-64
    22. Patrick Popescu-Pampu
      Pages 65-66
    23. Patrick Popescu-Pampu
      Pages 67-68
    24. Patrick Popescu-Pampu
      Pages 69-70
    25. Patrick Popescu-Pampu
      Pages 71-72
    26. Patrick Popescu-Pampu
      Pages 73-75
    27. Patrick Popescu-Pampu
      Pages 77-77
  3. Algebraic Surfaces

    1. Front Matter
      Pages 79-79
    2. Patrick Popescu-Pampu
      Pages 81-84
    3. Patrick Popescu-Pampu
      Pages 85-89
    4. Patrick Popescu-Pampu
      Pages 91-92
    5. Patrick Popescu-Pampu
      Pages 93-95
    6. Patrick Popescu-Pampu
      Pages 97-98
    7. Patrick Popescu-Pampu
      Pages 99-101
    8. Patrick Popescu-Pampu
      Pages 103-104
    9. Patrick Popescu-Pampu
      Pages 105-106
  4. Algebraic Surfaces

    1. Front Matter
      Pages 107-107
    2. Patrick Popescu-Pampu
      Pages 109-111
    3. Patrick Popescu-Pampu
      Pages 113-115
    4. Patrick Popescu-Pampu
      Pages 117-120
    5. Patrick Popescu-Pampu
      Pages 121-124
    6. Patrick Popescu-Pampu
      Pages 125-127
    7. Patrick Popescu-Pampu
      Pages 129-131
    8. Patrick Popescu-Pampu
      Pages 133-136
    9. Patrick Popescu-Pampu
      Pages 137-138
    10. Patrick Popescu-Pampu
      Pages 139-141
    11. Patrick Popescu-Pampu
      Pages 143-145
    12. Patrick Popescu-Pampu
      Pages 147-148

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

  • Patrick Popescu-Pampu
    • 1
  1. 1.UFR de MathématiquesUniversitè Lille 1Villeneuve d’AscqFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42312-8
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-42311-1
  • Online ISBN 978-3-319-42312-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site