Algebraic Geometry 1: From Algebraic Varieties to Schemes Kenji Ueno Publication Year: ISBN ISBN Kenji Ueno is a Japanese mathematician, specializing in algebraic geometry. He was in the s at the University of Tokyo and was from to a. Algebraic geometry is built upon two fundamental notions: schemes and sheaves . The theory of schemes was explained in Algebraic Geometry 1: From.

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If Griffiths-Harris is “algebraic geometry” then surely Huybrechts is as well! Steve Dalton marked it as to-read Sep 12, Excellent complete and advanced reference for surfaces. And indeed, there are a lot of high quality ‘articles’, and often you can find alternative approaches to a theory or a problem, which are more suitable for you.

At a far more abstract level, EGA’s are excellent, proofs are well detailed but intuition is completly absent. It is a classic and although algevraic flavor is clearly of typed concise notes, it is by far the shortest but thorough book on curves, which serves as a very nice introduction to the whole subject.

Kenji Ueno – Wikipedia

No trivia or quizzes yet. Fulton – “Intersection Theory”. It’s a research monograph and it’s unfinished, by the way. From Algebraic Varieties to Schemes.

Kenji Ueno

Could someone suggest me how to learn some basic theory of schemes? That’s a small thing, but hinders the reader from getting geometdy good understanding of these important concepts.


The material is illustrated by examples and figures, and some exercises provide the option to verify one’s progress. And Shafarevitch right now,to me,is your best bet for serious graduate students. I’m just warning that if you read it all the way through, you still won’t know the ‘basics’ of algebraic geometry.

I must admit that I find it almost unreadable, owing to the old-fashioned language. There are no discussion topics on this book yet. Very well done and indispensable for those needing a companion, but above all an expansion, to Hartshorne’s chapter.

It’s undoubtedly a real masterpiece- very user-friendly. Of course, by then, you are really wanting sheaves and line bundles!

Algebraic Geometry 1: From Algebraic Varieties to Schemes

We’d be able to produce a translation of EGA and other works fairly quickly. Ueno’s kenju is a self-contained introduction to this important circle of ideas, assuming only a knowledge of basic notions from abstract algebra such as prime ideals. It also provides some historical context.

Ideals, Varieties, and Algorithms: I asked around and was told to read Hartshorne. Shafarevich – “Basic Algebraic Geometry” vol. I totally, absolutely agree about Shafarevitch being the best textbook. I’ve been teaching an introductory uneo in algebraic geometry this semester and I’ve been looking at many sources.

Additional Material for the Book

Badescu – “Algebraic Surfaces”. Oh, I’m a big fan of the book. In addition, you can actually ask questions a feature thoroughly missed in e.


geometdy This was followed by another fundamental change in the s with Grothendieck’s introduction of schemes. Whereas it is actually not quite a textbook, it is becoming a very popular reference. Refresh and try again. The uniqueness claim is a bit strong: The Berkeley math dept requires its grad students to pass a language exam which consists of translating a page of math in French, German, or Russian into English.

Dear Andrew L, Why? Well, to be fair, this is only the first in a series of three books on the subject by the same author.

One of my favorites. Hope this makes my post more clear. Mukai’s Introduction to Invariants and Moduli surely deserves to be on this list.

Varieties in Projective Space also, for a more computational point of view Ideals, Varieties, and Algorithms: Dear Andrew L, Regarding your first comment: Yes, that’s much better.

The book is very complete and everything seems to be done “in the nicest way”. Nitin CR added it Nov 11, Very complete proves Riemann-Roch algebbraic curves in an easy language and concrete in classic constructions needed to understand the reasons about why things algebgaic done the way they are in advanced purely algebraic books.