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The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained.
The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.
List of contents
Preface.- Introduction.- Beginning concepts.- Schemes.- Properties of schemes.- Sheaves of modules.- Introduction to Cohomology.- Cohomology in algebraic geometry.- Exercises.
About the author
Igor Kriz is Professor of Mathematics at the University of Michigan in Ann Arbor, MI, USA
Sophie Kriz isHonors math major, LSA, at the University of Michigan in Ann Arbor, MI, USA
Summary
The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained.
The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.
Additional text
“The prerequisites to read this book are undergraduate analysis, algebra and topology. The proofs of all needed more advanced results of topology or algebra are given. The book is mainly self-contained; some proofs with all the necessary steps are proposed as exercises. … Each chapter ends with a set of exercises.” (Jean-Marc Drézet's, Mathematical Reviews, June, 2022)
“The present book is a very solid, and different than usual (or traditional), introduction to algebraic geometry that we can find on the market. … I can honestly recommend this item as a main reference for (advanced) courses devoted to algebraic geometry, and for extended courses devoted to introduction to algebraic geometry – this claim is based on the fact that the book is self-contained on the level of commutative algebra and due to this reason provides a coherent narration.” (Piotr Pokora, zbMATH 1471.14003, 2021)
Report
"The prerequisites to read this book are undergraduate analysis, algebra and topology. The proofs of all needed more advanced results of topology or algebra are given. The book is mainly self-contained; some proofs with all the necessary steps are proposed as exercises. ... Each chapter ends with a set of exercises." (Jean-Marc Drézet's, Mathematical Reviews, June, 2022)
"The present book is a very solid, and different than usual (or traditional), introduction to algebraic geometry that we can find on the market. ... I can honestly recommend this item as a main reference for (advanced) courses devoted to algebraic geometry, and for extended courses devoted to introduction to algebraic geometry - this claim is based on the fact that the book is self-contained on the level of commutative algebra and due to this reason provides a coherent narration." (Piotr Pokora, zbMATH 1471.14003, 2021)
