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The Rising Sea: Foundations Of Algebraic Geometry Ravi Vakil Princeton University Press
Scientific Books

The Rising Sea: Foundations Of Algebraic Geometry Ravi Vakil Princeton University Press

An accessible, motivating introduction to one of the most dynamic areas of mathematics. Decades ago, Mumford wrote that algebraic geometry "seems to have gained the reputation of an internal,...

An accessible, motivating introduction to one of the most dynamic areas of mathematics. Decades ago, Mumford wrote that algebraic geometry "seems to have gained the reputation of an internal, exclusive, and highly abstract field, with supporters secretly planning to understand all other mathematics." The revolution has now fully taken place and has...

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Genre: Oceanography Mathematics of Positive Sciences
165 63 €
166 Coins 166 Coins
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An accessible, motivating introduction to one of the most dynamic areas of mathematics. Decades ago, Mumford wrote that algebraic geometry "seems to have gained the reputation of an internal, exclusive, and highly abstract field, with supporters secretly planning to understand all other mathematics." The revolution has now fully taken place and has fundamentally changed the way we think about many fields of mathematics. This book provides a thorough foundation in the powerful ideas shaping the landscape today, with an informal yet rigorous presentation that builds intuition for understanding this fascinating machinery. It begins with a discussion of categorical thinking and sheaves, then develops the concepts of schemes and varieties as examples of "geometric spaces" before exploring their specific aspects. The book continues to cover topics such as dimension and smoothness, vector bundles and their natural generalizations, and significant cohomological tools and their applications. Important optional topics are included in sections marked with stars.

It offers a comprehensive introduction that is sure to become the standard on the subject. It contains a wealth of exercises allowing students to learn through practice. It requires few prerequisites, developing the tools students need to succeed, from category theory and sheaf theory to intersection and homological algebra. It uses an example-based approach that builds mathematical intuition. It is a standalone manual for graduate students and an essential reference for researchers.

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Publisher
Princeton University Press
Type
Oceanography, Mathematics and Natural Sciences
Language
English
Subtitle
-
Cover
Hardcover
Number of Pages
688
Release Date
21/10/2025
Publication Date
2025
Dimensions
-
ISBN-13
9780691268668

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