Synopsis
This book explores the complex world of Riemann surfaces, delving into their intricate geometry and the fascinating interplay between their properties and the functions that define them. Building upon the author's previous work, the book offers a rigorous examination of holomorphic differentials—functions crucial to understanding the behavior of these surfaces—and their relationship to the underlying geometric structures. The book utilizes a unique approach, visualizing the space of Riemann surfaces as a bounded domain within complex number space. This powerful representation allows for a deeper analysis of the relationships between the moduli—parameters that govern the shape of these surfaces—and the associated holomorphic differentials. This approach provides a unified framework for understanding the interplay between geometry and analysis in this area of mathematics. The author also investigates the role of Weierstrass points—special points on Riemann surfaces—and their connection to the moduli. Furthermore, the book explores the connections between the theory of Riemann surfaces and the theory of algebraic curves, showcasing the fundamental role that these surfaces play in understanding the structure of these important geometric objects. The book concludes with a discussion of the mapping of Teichmüller space, a fundamental space in the theory of Riemann surfaces, into the Siegel space of symmetric matrices, highlighting the deep and elegant relationships that exist between these complex mathematical structures.
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Holomorphic Differentials as Functions of Moduli (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book explores the complex world of Riemann surfaces, delving into their intricate geometry and the fascinating interplay between their properties and the functions that define them. Building upon the author's previous work, the book offers a rigorous examination of holomorphic differentialsââ âfunctions crucial to understanding the behavior of these surfacesââ âand their relationship to the underlying geometric structures. The book utilizes a unique approach, visualizing the space of Riemann surfaces as a bounded domain within complex number space. This powerful representation allows for a deeper analysis of the relationships between the moduliââ âparameters that govern the shape of these surfacesââ âand the associated holomorphic differentials. This approach provides a unified framework for understanding the interplay between geometry and analysis in this area of mathematics. The author also investigates the role of Weierstrass pointsââ âspecial points on Riemann surfacesââ âand their connection to the moduli. Furthermore, the book explores the connections between the theory of Riemann surfaces and the theory of algebraic curves, showcasing the fundamental role that these surfaces play in understanding the structure of these important geometric objects. The book concludes with a discussion of the mapping of Teichmüller space, a fundamental space in the theory of Riemann surfaces, into the Siegel space of symmetric matrices, highlighting the deep and elegant relationships that exist between these complex mathematical structures. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781334016127_0
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Holomorphic Differentials as Functions of Moduli Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LX-9781334016127
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Holomorphic Differentials as Functions of Moduli Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LX-9781334016127
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