海平面上升：代数几何基础 The Rising Sea: Foundations of Algebraic Geometry

基本信息

ISBN-13：9780691268675

ISBN-10：0691268673

Author：Ravi Vakil

Publisher：Princeton University Press

Imprint：Princeton University Press

Format：Paperback

Number of Pages：688

Release Date：27 January 2026

Weight：1.39kg

Dimensions：45mm x 254mm x 181mm

信息仅供参考，具体请以实物为准

书籍简介

本书以平易近人、引人入胜的方式，介绍了数学中具活力的领域之一——代数几何。

几十年前，芒福德曾写道，代数几何“似乎已经落得个深奥、排外、抽象的名声，仿佛其拥趸们正密谋着要掌控数学的其他所有领域。”如今，这场变革已然全面到来，从根本上改变了我们对许多数学领域的思考方式。本书以通俗易懂却又严谨的阐述，为读者奠定了塑造当今数学格局的强大思想基础，并帮助读者建立理解这些复杂机制的直觉。本书先探讨范畴论和层，然后发展概型和簇的概念，作为“几何空间”的例证，并进一步讨论它们的具体方面。本书还涵盖了诸如维数和光滑性、向量丛及其自然推广、以及重要的上同调工具及其应用等主题。一些重要的可选主题以星号标注的章节列出。

·本书全面深入地介绍了该领域，将成为该领域的标准之作。

·书中包含大量练习，使学生能够在实践中学习。

·本书对先修知识的要求不高，从范畴论、层论到交换代数和同调代数，全面培养学生所需的技能。

·本书采用实例驱动的教学方法，帮助学生建立数学直觉。

·本书既是研究生的自学教材，也是研究人员的重要参考资料。

An accessible, motivated introduction to one of the most dynamic areas of mathematics

Decades ago, Mumford wrote that algebraic geometry “seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics.” The revolution has now fully come to pass and has fundamentally changed how we think about many fields of mathematics. This book provides a thorough foundation in the powerful ideas that now shape the landscape, with an informal yet rigorous exposition that builds intuition for understanding the formidable machinery. It begins with a discussion of categorical thinking and sheaves and then develops the notion of schemes and varieties as examples of “geometric spaces” before discussing their specific aspects. The book goes on to cover topics such as dimension and smoothness, vector bundles and their natural generalizations, and important cohomological tools and their applications. Important optional topics are included in starred sections.

Provides a comprehensive introduction certain to become the standard on the subject

Features a wealth of exercises that enable students to learn by doing

Requires few prerequisites, developing the tools students need to succeed, from category theory and sheaf theory to commutative and homological algebra

Uses an example-driven approach that builds mathematical intuition

Is a self-contained textbook for graduate students and an essential reference for researchers

作者简介

拉维·瓦基尔是斯坦福大学罗伯特·格里梅特数学教授，也是美国数学学会主席。他是《数学马赛克：模式与问题解决》一书的作者。

Ravi Vakil is the Robert Grimmett Professor of Mathematics at Stanford University and president of the American Mathematical Society. He is the author of A Mathematical Mosaic: Patterns and Problem Solving.