An Undergraduate Primer in Algebraic Geometry

This book provides an introduction to basic concepts in algebraic geometry, including affine and projective varieties, curves, and the theory of divisors. It is suitable for undergraduate courses and includes exercises with solutions.

Format: Paperback / softback
Length: 327 pages
Publication date: 05 May 2021
Publisher: Springer Nature Switzerland AG

This comprehensive text offers a thorough introduction to algebraic geometry, encompassing two distinct parts. The first part delves into the fundamental concepts of affine and projective varieties, exploring their characteristics, properties, and notable examples. The second part focuses on the theory of curves, encompassing local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors, and linear series.

The approach adopted in this book is purely algebraic, utilizing commutative algebra as the primary tool to derive the required results, often accompanied by proofs. The prerequisites for this text include a solid foundation in affine and projective geometry, basic algebraic concepts related to rings, modules, fields, linear algebra, fundamental notions in the theory of categories, and some elementary point-set topology.

This book serves as an excellent textbook for undergraduate courses in algebraic geometry. While its primary audience is not necessarily aspiring algebraic geometers, it can be valuable to interested students and researchers seeking a foundational understanding of the topic. Additionally, the book includes numerous exercises, providing further examples and extending the theory in areas not fully developed in the text. Solutions to select exercises are provided at the end of each chapter.

By presenting the material in a clear and concise manner, this book aims to facilitate a deeper comprehension of algebraic geometry and its applications. Whether you are a student embarking on this mathematical journey or a researcher seeking to expand your knowledge in the field, this text will undoubtedly be a valuable resource.

Weight: 572g
Dimension: 155 x 235 x 20 (mm)
ISBN-13: 9783030710200
Edition number: 1st ed. 2021