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
ftp://www.msri.org/pub/publications/books/SLAG.

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.