Algebraic Geometry, Part II Lent 2009

This is an augmented and annotated reading list for the course. The eagle-eyed will have noticed that the course description in the Part II booklet advises browsing the books by Kirwan and Reid in the schedules, yet they are not to be found there. This page aims to remedy this omission and to add notes about the level of the various texts available. Prices are taken from (on 15th November).

  1. K. Hulek, Elementary Algebraic Geometry (paperback, £17).
    This is probably the closest book to the style and content of the lectures. Chapters 1-4 and 6 cover the schedule.
  2. F. Kirwan, Complex Algebraic Curves (paperback, £16)
    This covers much of the material on curves, although in this book there is more of an emphasis on plane curves, and on topological rather than algebraic ideas.
  3. M. Reid, Undergraduate Algebraic Geometry (paperback, £14)
    Written in a characteristic style which may either amuse or irritate, this text is an excellent insightful general introduction to algebraic geometry, and covers much of the schedule.
  4. B. Hassett, Introduction to Algebraic Geometry (paperback, £19)
    An interesting first course on algebraic geometry, from the point of view of computation. It develops the algorithms (notably the theory of Groebner Bases) in algebra needed to perform explicit computations in algebraic geometry.
  5. K. Ueno, Introduction to Algebraic Geometry (hardback £49 from Blackwells but currently (Nov 2008) unavailable)
    A slightly more advanced introductory book, which covers the schedule and quite a bit more. (Not to be confused with the much more advanced books by the same author.)
  6. R. Hartshorne, Algebraic Geometry (hardback £44)
    The classic introductory text to scheme theory, famous for its numerous, and sometimes taxing, exercises. If you are going to study algebraic geometry as a graduate student you will want this. There is a cheaper paperback edition, although your copy may become so well-used that the pages fall out. Most students taking the Part II course will find this book far too advanced.