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Meromorphic Functions and Projective Curves

  • Kichoon Yang

Part of the Mathematics and Its Applications book series (MAIA, volume 464)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Kichoon Yang
    Pages 1-35
  3. Kichoon Yang
    Pages 37-53
  4. Kichoon Yang
    Pages 55-97
  5. Kichoon Yang
    Pages 99-123
  6. Kichoon Yang
    Pages 125-167
  7. Kichoon Yang
    Pages 169-196
  8. Back Matter
    Pages 197-207

About this book

Introduction

This book contains an exposition of the theory of meromorphic functions and linear series on a compact Riemann surface. Thus the main subject matter consists of holomorphic maps from a compact Riemann surface to complex projective space. Our emphasis is on families of meromorphic functions and holomorphic curves. Our approach is more geometric than algebraic along the lines of [Griffiths-Harrisl]. AIso, we have relied on the books [Namba] and [Arbarello-Cornalba-Griffiths-Harris] to agreat exten- nearly every result in Chapters 1 through 4 can be found in the union of these two books. Our primary motivation was to understand the totality of meromorphic functions on an algebraic curve. Though this is a classical subject and much is known about meromorphic functions, we felt that an accessible exposition was lacking in the current literature. Thus our book can be thought of as a modest effort to expose parts of the known theory of meromorphic functions and holomorphic curves with a geometric bent. We have tried to make the book self-contained and concise which meant that several major proofs not essential to further development of the theory had to be omitted. The book is targeted at the non-expert who wishes to leam enough about meromorphic functions and holomorphic curves so that helshe will be able to apply the results in hislher own research. For example, a differential geometer working in minimal surface theory may want to tind out more about the distribution pattern of poles and zeros of a meromorphic function.

Keywords

Divisor Grad Meromorphic function algebraic curve differential geometry

Authors and affiliations

  • Kichoon Yang
    • 1
  1. 1.Department of MathematicsUniversity of Texas — Pan AmericanEdinburgUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9151-5
  • Copyright Information Springer Science+Business Media Dordrecht 1999
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5149-3
  • Online ISBN 978-94-015-9151-5
  • Buy this book on publisher's site