Overview
- Provides a self contained introduction to Algebraic Geometry for undergraduate students
- Contains many exercises, some of them with solution
- Useful for non-experts who want to learn the basics of Algebraic Geometry
Part of the book series: UNITEXT (UNITEXT, volume 129)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
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Table of contents (20 chapters)
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Front Matter
Keywords
About this book
This book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems.
The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology.
This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic.
The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter.
Reviews
“New concepts in algebra that one needs, in order to understand the content of the book, are introduced … . I find this feature as an asset of the present book. … the present book is a valuable introduction to algebraic geometry which is nicely written … and a pleasure to read. It can be recommended as a first book for undergraduate courses devoted to algebraic geometry, and also as a supplementary source for standard courses devoted to algebraic geometry.” (Piotr Pokora, zbMATH 1471.14001, 2021)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: An Undergraduate Primer in Algebraic Geometry
Authors: Ciro Ciliberto
Series Title: UNITEXT
DOI: https://doi.org/10.1007/978-3-030-71021-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Softcover ISBN: 978-3-030-71020-0Published: 05 May 2021
eBook ISBN: 978-3-030-71021-7Published: 05 May 2021
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 1
Number of Pages: XI, 327
Number of Illustrations: 1 b/w illustrations
Topics: Geometry, Projective Geometry, Algebra