Introductory books about algebraic geometry:

• Algebraic Geometry : A First Course, by J. Harris. (Our text for Fall and Winter quarters.)
• Basic Algebraic Geometry, by I.R. Shafarevich. It includes a brief introduction to scheme theory.
• Introduction to algebraic geometry (preliminary version of first 3 chapters), by D. Mumford. Lecture notes, available in the library. Reissued as The red book of varieties and schemes, Springer-Verlag, 1988. {Lecture Notes in Mathematics #1358}
• Algebraic Curves, by W. Fulton. Contains basic results about varieties, and some useful introductory topics in commutative algebra.
• Algebraic Curves , by R. Walker. Some overlap with Fulton's book, but a different (more classical) approach to many topics.
• Undergraduate algebraic geometry, by M. Reid. This book includes self-contained proofs of several famous classical theorems. The title may be too optimistic, but the approach is relatively accessible.

Books about commutative algebra and algebraic approaches to algebraic geometry:

• Algebraic Geometry, by R. Hartshorne. An excellent reference work. Chapter I contains a lot of material aboout varieties but requires some familiarity with commutative algebra. Chapters II and III are about schemes and sheaf cohomology respectively. In the remaining chapters, this material is applied to the study of curves and surfaces.
• Schemes : the language of modern algebraic geometry, by D.Eisenbud and J. Harris. An introduction to the theory of schemes.
• Introduction to Algebraic Geometry and Commutative Algebra, by E. Kunz. Includes some material not in other introductory books. It is fairly accessible.
• Introduction to Commutative Algebra , by M. Atiyah and I.G. Macdonald. This is a very good introductory book about this subject, and is one of the more readable ones.
• Commutative Algebra, by H. Matsumura. Somewhat more comprehensive than the book by Atiyah and Macdonald. It is fairly readable, although slightly more challenging than Atiyah & Macdonald.
• Algebra, by S. Lang (3^rd edition). Useful sections include Chapter IX (Algebraic Spaces) and Chapter X (Noetherian Rings and Modules).
• Basic Algebra II, by N. Jacobson, especially Chapter 7.
• Commutative Algebra , by O. Zariski and P. Samuel. A classic two-volume work, spanning the range from first-year graduate level topics to relatively advanced topics.
• Local Rings, by M. Nagata. Somewhat difficult to read, but contains much information not available in other books.

Books about complex analytic approaches to algebraic geometry:

• Elementary Algebraic Geometry, by K. Kendig. A very introductory account of some of the topological properties of complex algebraic varieties.
• Algebraic Geometry I : Complex Projective Varieties, by D. Mumford. An introduction to algebraic geometry from a complex analytic viewpoint. Contains many penetrating insights typical of Mumford's writings, but the reader has to fill in some details.
• Principles of Algebraic Geometry, by P. Griffiths and J. Harris. An extensive account of algebraic geometry over the complex numbers, approached via the theory of complex manifolds.

Prof. Joel Roberts
Office: 351 Vincent Hall
Phone: (612) 625-1076
Dept. FAX: (612) 626-2017
e-mail: roberts@math.umn.edu
http://www.math.umn.edu/~roberts