Principles of Complex Analysis

This textbook covers complex analysis, intended for upper undergraduate or beginning graduate students, focusing on essential topics for those studying algebraic geometry. It presents abstract concepts only when necessary, with a rigorous but elementary exposition. The chapter on Riemann surfaces includes key results on compact Riemann surfaces, particularly for elliptic curves.

Format: Paperback / softback
Length: 257 pages
Publication date: 28 September 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook on complex analysis is meticulously crafted with the utmost care to cater to the needs of upper undergraduate or early graduate students embarking on the captivating realm of algebraic geometry and its related subjects. The author places paramount emphasis on the facets of complex analysis that hold immense significance for those aspiring to delve into the intricacies of algebraic geometry. The exposition is rigorous yet accessible, ensuring that abstract concepts are introduced only when absolutely necessary, thereby fostering a deep understanding and motivation among readers. By adopting this approach, the author encourages the reader to gradually embrace more abstract definitions, such as those of sheaves or line bundles, which may not be explicitly mentioned in the book but are crucial for those ready to delve into such higher levels of abstraction.

In the chapter dedicated to Riemann surfaces, a series of pivotal results are stated and meticulously proved, focusing on the first nontrivial case, which involves elliptic curves. These results lay the foundation for further exploration and understanding of the complex world of Riemann surfaces.

Throughout the textbook, numerous examples and exercises are provided to aid in comprehension and application of the theoretical concepts. These exercises range in difficulty, allowing students to gradually build their skills and confidence as they progress through the material. Additionally, comprehensive solutions are provided, enabling students to verify their understanding and gain a deeper grasp of the subject matter.

Whether you are a student seeking to expand your knowledge in complex analysis or a professional looking to deepen your understanding of algebraic geometry, this textbook is an invaluable resource. Its clear and concise writing style, coupled with extensive explanations and carefully designed exercises, makes it an ideal guide for anyone interested in this field. So, embark on this intellectual journey and explore the wonders of complex analysis with confidence and enthusiasm.

Weight: 421g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030593674
Edition number: 1st ed. 2020