Buch, Englisch, 208 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 341 g
Buch, Englisch, 208 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 341 g
Reihe: Mathematics and Its Applications
ISBN: 978-90-481-5149-3
Verlag: Springer Netherlands
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.
Zielgruppe
Research
Fachgebiete
Weitere Infos & Material
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.
