Meromorphic Functions and Projective Curves

Kichoon Yang

ISBN 10: 0792355059 / ISBN 13: 9780792355052

Editore: Springer, Springer, 1998

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9780792355052

Dati bibliografici

• Titolo: Meromorphic Functions and Projective Curves
• Editore: Springer, Springer
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0792355059
• ISBN 13: 9780792355052
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 16 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 16 millimetri di profondità
• Peso: 500 grammi

Descrizione articolo

Riassunto

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.

Contenuti

Preface. 1. Foundational Material. 2. Analytic and Algebraic Families. 3. Meromorphic Functions. 4. Brill-Noether Theory. 5. Projective Differential Geometry. 6. Metric Geometry of Curves. Bibliography. Index.