From Holomorphic Functions to Complex Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2002
|
| Schriftenreihe: | Graduate Texts in Mathematics
213 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is an introduction to the theory of complex manifolds. The author's intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible. Therefore, the abstract concepts involving sheaves, coherence, and higher-dimensional cohomology have been completely avoided. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Nevertheless, deep results can be proved, for example the Remmert-Stein theorem for analytic sets, finiteness theorems for spaces of cross sections in holomorphic vector bundles, and the solution of the Levi problem. Each chapter is complemented by a variety of examples and exercises. The only prerequisite needed to read this book is a knowledge of real analysis and some basic facts from algebra, topology, and the theory of one complex variable. The book can be used as a first introduction to several complex variables as well as a reference for the expert. Klaus Fritzsche received his PhD from the University of Göttingen in 1975, under the direction of Professor Hans Grauert. Since 1984, he has been Professor of Mathematics at the University of Wuppertal, where he has been investigating convexity problems on complex spaces and teaching undergraduate and graduate courses on Real and Complex Analysis. Hans Grauert studied physics and mathematics in Mainz, Münster and Zürich. He received his PhD in mathematics from the University of Münster and in 1959 he became a full professor at the University of Göttingen. Professor Grauert is responsible for many important developments in mathematics in the Twentieth Century. Along with Reinhold Remmert, Karl Stein and Henri Cartan, he founded the theory of Several Complex Variables in its modern form. He also proved various important theorems, including Levi's Problem and the coherence of higher direct image sheaves. Professor Grauert is the author of 10 books and his Selected Papers was published by Springer in 1994 |
| Beschreibung: | 1 Online-Ressource (XVI, 398 p) |
| ISBN: | 9781468492736 9781441929839 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-9273-6 |
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| 500 | |a The book can be used as a first introduction to several complex variables as well as a reference for the expert. Klaus Fritzsche received his PhD from the University of Göttingen in 1975, under the direction of Professor Hans Grauert. Since 1984, he has been Professor of Mathematics at the University of Wuppertal, where he has been investigating convexity problems on complex spaces and teaching undergraduate and graduate courses on Real and Complex Analysis. Hans Grauert studied physics and mathematics in Mainz, Münster and Zürich. He received his PhD in mathematics from the University of Münster and in 1959 he became a full professor at the University of Göttingen. Professor Grauert is responsible for many important developments in mathematics in the Twentieth Century. Along with Reinhold Remmert, Karl Stein and Henri Cartan, he founded the theory of Several Complex Variables in its modern form. | ||
| 500 | |a He also proved various important theorems, including Levi's Problem and the coherence of higher direct image sheaves. Professor Grauert is the author of 10 books and his Selected Papers was published by Springer in 1994 | ||
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Datensatz im Suchindex
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| building | Verbundindex |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-9273-6 |
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| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 9781468492736 9781441929839 |
| issn | 0072-5285 |
| language | English |
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| spelling | Fritzsche, Klaus Verfasser aut From Holomorphic Functions to Complex Manifolds by Klaus Fritzsche, Hans Grauert New York, NY Springer New York 2002 1 Online-Ressource (XVI, 398 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 213 0072-5285 This book is an introduction to the theory of complex manifolds. The author's intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible. Therefore, the abstract concepts involving sheaves, coherence, and higher-dimensional cohomology have been completely avoided. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Nevertheless, deep results can be proved, for example the Remmert-Stein theorem for analytic sets, finiteness theorems for spaces of cross sections in holomorphic vector bundles, and the solution of the Levi problem. Each chapter is complemented by a variety of examples and exercises. The only prerequisite needed to read this book is a knowledge of real analysis and some basic facts from algebra, topology, and the theory of one complex variable. The book can be used as a first introduction to several complex variables as well as a reference for the expert. Klaus Fritzsche received his PhD from the University of Göttingen in 1975, under the direction of Professor Hans Grauert. Since 1984, he has been Professor of Mathematics at the University of Wuppertal, where he has been investigating convexity problems on complex spaces and teaching undergraduate and graduate courses on Real and Complex Analysis. Hans Grauert studied physics and mathematics in Mainz, Münster and Zürich. He received his PhD in mathematics from the University of Münster and in 1959 he became a full professor at the University of Göttingen. Professor Grauert is responsible for many important developments in mathematics in the Twentieth Century. Along with Reinhold Remmert, Karl Stein and Henri Cartan, he founded the theory of Several Complex Variables in its modern form. He also proved various important theorems, including Levi's Problem and the coherence of higher direct image sheaves. Professor Grauert is the author of 10 books and his Selected Papers was published by Springer in 1994 Mathematics Global analysis (Mathematics) Differential equations, partial Analysis Several Complex Variables and Analytic Spaces Mathematik Holomorphe Funktion (DE-588)4025645-5 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 s 1\p DE-604 Holomorphe Funktion (DE-588)4025645-5 s 2\p DE-604 Grauert, Hans Sonstige oth https://doi.org/10.1007/978-1-4684-9273-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fritzsche, Klaus From Holomorphic Functions to Complex Manifolds Mathematics Global analysis (Mathematics) Differential equations, partial Analysis Several Complex Variables and Analytic Spaces Mathematik Holomorphe Funktion (DE-588)4025645-5 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd |
| subject_GND | (DE-588)4025645-5 (DE-588)4031996-9 |
| title | From Holomorphic Functions to Complex Manifolds |
| title_auth | From Holomorphic Functions to Complex Manifolds |
| title_exact_search | From Holomorphic Functions to Complex Manifolds |
| title_full | From Holomorphic Functions to Complex Manifolds by Klaus Fritzsche, Hans Grauert |
| title_fullStr | From Holomorphic Functions to Complex Manifolds by Klaus Fritzsche, Hans Grauert |
| title_full_unstemmed | From Holomorphic Functions to Complex Manifolds by Klaus Fritzsche, Hans Grauert |
| title_short | From Holomorphic Functions to Complex Manifolds |
| title_sort | from holomorphic functions to complex manifolds |
| topic | Mathematics Global analysis (Mathematics) Differential equations, partial Analysis Several Complex Variables and Analytic Spaces Mathematik Holomorphe Funktion (DE-588)4025645-5 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Differential equations, partial Analysis Several Complex Variables and Analytic Spaces Mathematik Holomorphe Funktion Komplexe Mannigfaltigkeit |
| url | https://doi.org/10.1007/978-1-4684-9273-6 |
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