Course Announcement
UC Berkeley, Fall Semester 1999

Math 256A: Algebraic Geometry

Instructor: Bernd Sturmfels (bernd@math, Evans 701)

Time: Tuesdays and Thursdays 9:30-11:00am
Place: 5 Evans Hall

This course provides an introduction to modern algebraic geometry. We will study algebraic varieties by developing the language of schemes right from of the start of the class. Most of the lectures will follow the required text book

David Eisenbud, Joe Harris: "The Geometry of Schemes", Springer Graduate Texts, to appear in 1999.

This book has not appeared yet, and the publisher has given permission to make copies available for the students in this class. You can buy these course notes at Copy Central (Euclid/Hearst) or download them the site

The prerequisites for this course are a solid foundation in undergraduate abstract algebra, willingness to work hard on concrete problems (such as the study of varieties and schemes with the help of computer algebra), and knowledge of elementary commutative algebra and projective geometry at the level of Chapters 8 and 9 in

David Cox, John Little, Donal O'Shea: "Ideals, Varieties and Algorithms", Springer Undergraduate Texts, 1997.

Having taken Math 250AB or Math 255 is useful but not essential. First-year mathematics graduate students can take this class and Math 250 in parallel, but they are advised to talk to both instructors before the first day of classes.

For additional reading there are twelve books on reserve at the math library in the fall of 1999.

The course grade will be based on the weekly homework and the final exam. You can download the homework assignments:
Homework 1, due August 31 (in tex format or postscript )
Homework 2, due September 7 (in tex format or postscript )
Homework 3, due September 14 (in tex format or postscript )
Homework 4, due September 21 (in tex format or postscript )
Homework 5, due October 5 (in tex format or postscript )
Homework 6, due October 12 (in tex format or postscript )
Homework 7, due October 19 (in tex format or postscript )
Homework 8, due October 26 (in tex format or postscript )
Homework 9, due November 2 (in tex format or postscript )
Homework 10, due November 9 (in tex format or postscript )
Homework 11, due November 16 (in tex format or postscript )

Take Home Final Exam , due November 30 tex format or postscript )

The continuation of this course in the Spring of 2000 will focus on the study of toric varieties, flag varieties and Hilbert schemes. These special varieties appear frequently in applications of algebraic geometry (for instance, in mathematical physics or combinatorics). Math 256B will be somewhat independent from Math 256A this time.