![]() It is expected for the lecture and the exam that a majority of the problems have been worked on. It is also encouraged to hand them in as it gives you (hopefully) valuable feedback. Understanding the material and concepts of the course and it is for your own benefit to work on the problems. Nevertheless, the exercises are essential for ![]() Testat conditions: The testat condition was temporarily suspended ( see here). He enjoys vacationing at Disneyworld and visiting the land of algebraic geometry, but plans to remain a probabilist.First lecture: Tuesday, February 18, 2014įirst exercise class : Friday, February 21, 2014 When not working, he likes to eat spicy food, and does not enjoy losing money at casinos. Peter Rabinovitch is a Systems Architect at Research in Motion, and a PhD student in probability. There is such a huge range of material to cover, so many different viewpoints, and so many books and notes available on the web that choosing just one to follow would be like eating only one item at an all you can eat buffet. In fact, to somebody trying to learn algebraic geometry, the best advice I can offer is that the key word in the previous sentence is “and”. Perhaps it is just a manifestation of the maxim that the best math book on any topic is the third one that you read, but I found these books to be the best ones I’ve read on algebraic geometry.Īfter reading Basic Algebraic Geometry, next steps might include Hartshorne’s book Algebraic Geometry and/or Ravi Vakil’s notes. The first book has an appendix on various algebraic concepts, and the second concludes with a nice historical sketch of a dozen or so pages. There are many exercises, most of them interesting and doable. In particular, the subject of schemes has a fearsome reputation, but at least at this level of generality, the explanations are clear and well motivated. It feels like the author is right beside you, explaining things as you go. ![]() The prose is excellent it is hard to believe it is a translation. The book has a nice pace there are many examples and pictures that help solidify the ideas in the reader’s mind. The complete tables of contents can be found on Google Books. Shafarevich’s Basic Algebraic Geometry is now in two volumes, the first dealing with classical topics, namely varieties in projective space the second volume discussing schemes and complex manifolds. Other than that, not much else is required, other than lots of paper and pencils. Depending on your background, you might also need a topology text nearby, but nothing too fancy (as Basic Algebraic Geometry does not cover cohomology). In fact, both these books have nice introductory sections on algebraic geometry. To start reading Basic Algebraic Geometry, the reader should be comfortable with algebra at the level of Artin’s Algebra, or Dummit and Foote’s Abstract Algebra. There are several papers in the Princeton Companion to Mathematics that are excellent, in particular, Ellenberg’s article on Arithmetic Geometry has a great introduction to what schemes are and why they are useful (and it is available on line). Smith’s An Invitation to Algebraic Geometry is a tasty introduction - if after looking through it you are not interested in algebraic geometry, I don’t think you ever will be. I am familiar with Reid’s Undergraduate Algebraic Geometry, which is nice and entertaining. There are many excellent introductions on the subject at a range of levels. Basic Algebraic Geometry fills that role beautifully. I have no plans to switch from probability to algebraic geometry, but I wanted more than an introduction to the subject. ![]() For some reason, I found myself attracted to the field, wanting to know what it was all about. So, what in the world is a probability PhD student doing reviewing Shafarevich’s two-volume Basic Algebraic Geometry? Good question. ![]()
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