Sinossi
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.
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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.
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Book by Kichoon Yang
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Meromorphic Functions and Projective Curves (Mathematics and Its Applications)
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Meromorphic functions and projective curves.
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Meromorphic Functions and Projective Curves
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 220 pp. Englisch. Codice articolo 9780792355052
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 . Codice articolo 5968707
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Meromorphic Functions and Projective Curves
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ISBN 13: 9780792355052
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 220 pp. Englisch. Codice articolo 9780792355052
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