Meromorphic Functions and Projective Curves: 464 (Mathematics and Its Applications, 464) - Hardcover

Kichoon Yang

Hardcover

ISBN 10: 0792355059 ISBN 13: 9780792355052

Publisher: Springer, 1998

Synopsis

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.

About this title

Synopsis

The main purpose of this volume is to give an exposition of various aspects of meromorphic functions and linear series on algebraic curves, with some emphasis on families of meromorphic functions. It is written in such a way as to facilitate their applications in other areas of mathematics. Meromorphic functions on a compact Riemann surface, or, more generally, holomorphic curves and linear series, have numerous applications in many different areas of mathematics. This work gives a concise survey of results in the elementary theory of meromorphic functions and divisors on curves, and makes these results more accessible to students and non-experts, in particular differential geometers. This volume should be of interest to graduate students and researchers in mathematics, especially in algebraic and differential geometry.

Edition details

• Publisher: Springer
• Publication date: 1998
• Language: English
• ISBN 10: 0792355059
• ISBN 13: 9780792355052
• Binding: Hardcover
• Number of pages: 216