An Invitation to Algebraic Geometry (Universitext) 1st Edition by Karen E. Smith (PDF)

Description

This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

User’s Reviews

Editorial Reviews: Review K.E. Smith, L. Kahanpaeae, P.Kekaelaeinen, and W.N. TravesAn Invitation to Algebraic Geometry”The book . . . is clear and accessible.”―CHOICE

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This could be your only book on algebraic geometry if you just want a sound idea of what algebraic geometry can do. If you actually want to know the field, and you do not already have a lot of expert friends telling you about it, then the advanced books will go much more easily with this expert around. It is a terrific guide to the key ideas–what they mean, how they work, how they look.The only book like this one in brevity and scope is Reid UNDERGRADUATE ALGEBRAIC GEOMETRY–with its highly informed, highly polemical, final chapter on the state of the art. Both are very good. This one is more advanced. Beyond what Reid covers, Smith sketches Hilbert polynomials, Hironaka’s (and very briefly even De Jong’s) approach to removing singularities, and ample line bundles. You do need a bit of topology and analysis to follow it. Smith has very many fewer concrete examples than Reid. They are beautifully chosen classics, like Veronese maps and Segre maps, so they teach a lot. And the more you know to start with, the more you will see in each.The book does geometry over the complex numbers. It is good old conservative material, with terrific graphics of curves and surfaces. The proofs and partial proofs are very clear, intuitive and to the point. But, in fact, just because the proofs are so clear and to the point they usually work in a much broader setting. Long stretches of the book apply just as well over any field or any algebraically complete field. This generality is only mentioned a few times, in passing, but is there if you want it. Smith describes schemes very briefly, and mentions them at each point where they naturally arise. You will not know what schemes “are” at the end of this book. You will know some things they DO. She has no time for fights between “concretely complex” and “abstractly scheming” approaches–for her it is all geometry.

⭐This book sets aside a lot of the tedious background required to get started in algebraic geometry and lets you get acquainted with the actual ideas of the subject. The section on vector bundles at the end could stand to be a little longer, but it’s the best book on algebraic geometry that I know of.

⭐I have only some knowledge on differential geometry and algebraic topology. This is a very good starting material for my level. I can understand the content easily. This book focuses on the key ideas of the topic, without being bothered by the algebraic details.

⭐For people just starting on Algebraic Geometry, Robin Hartshorne’s book, is very daunting–but it is the ULTIMATE book for professional and advanced readers. But for starters, Karen Smith’s “An Invitation to Algebraic Geometry” is simply a SPLENDID way to start working on the basic ideas. The author has some stunning graphs and pictures to help understand material. I loved the book the minute I opened it. BUY it NOW!

⭐This book gives you the absolute basics of what Algebraic Geometry is. But if you are looking to do research in this area, the book is terse and sometimes just not helpful. Make sure you have topology or can pick it up before you buy this book.

⭐Whenever you find four authors on a volume as thin as this,you know trouble is brewing. Algebraic geometry is a difficultsubject which requires a copious number of examples to evenkeep the terms straight. Otherwise, the exposition degeneratesinto an empty string of definitions. The so called ‘chapters’ herebarely scratch the surface and it is not at all clear why anyonebothered to collect them into book form. You can find as muchor more detail in the relevant Wikipedia articles and vastly morein countless course notes which have been posted on the web.This is hardly a book worth reading and certainly not worth owning.

⭐excellent book … can make learning algebraic geometry as easy as bedside reading … highly recommended.

⭐Le sujet est complexe et pourtant les quatre auteurs introduisent les différents concepts du sujet avec beaucoup de pédagogie, rendant la lecture très digeste. Un grand bravo pour cette introduction qui me permit à l’époque de m’orienter pour le choix du DEA (master 2 pour les plus jeunes).

⭐

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