Office: Van Vleck 413
Telephone: 262 - 3545
email: sottile@math.wisc.edu
WWW:
http://www.math.wisc.edu/~sottile
Office: Van Vleck 413
Telephone: 262 - 3545
email: sottile@math.wisc.edu
WWW:
http://www.math.wisc.edu/~sottile
Hartshorne, Algebraic Geometry.
Mumford, Algebraic Geometry I:
Complex Projective Varieties
Fulton, Algebraic Curves.
Zariski & Samuel, Commutative Algebra.
Eisenbud, Commutative Algebra with a view towards Algebraic
Geometry.
Mumford, The Little Red Book of
Varieties and Schemes.
Griffiths and Harris, Principles of
Algebraic Geometry.
Our Text.
Harris, Algebraic Geometry.
Atiyah & Macdonald, Commutative Algebra.
Matusumora, Commutative Ring Theory.
Algebraic Geometry is concerned with the study of solutions to systems of polynomial equations. This simplistic statement accentuates its importance (solving systems of polynomials is a ubiquitous problem in mathematics) and also misrepresents the subtlety and richness in the interplay between geometry and algebra in the subject.
This course will follow the standard text of Shafarevich, which emphasizes the algebraic aspects of algebraic geometry. To provide a balance with its other aspects, we will study many concrete geometric examples, at times with computational techniques.
For further information, or if you are interested in this course, please contact me at sottile@math.wisc.edu or in my office (vV 413).
One advantage to the text of Shafarevich is that it has so many, very doable exercises. When I began studying algebraic geometry, I did them all. While that would be great if everyone could do that, I am realistic and will expect much less. However, you can learn a great deal by doing, so I do want my students to work on a good number of the problems.
We will have 4 problem sets in all. Two will be graded (Second (written) problem set due 22 October.), and 2 will be presented by members of the class to the rest of us at 2 evening problem sessions These problem sessions will make up for the lectures of 23 September, and 26 and 28 October, which I must miss.
I also hope to take advantage of recent technology and study some examples using tools from computational algebraic geometry. I have in mind that we will all become somewhat familiar with MACAULAY2, a freely available and very powerful computer algebra package purpose built as a tool for working in algebraic geometry.
The first homework will be discussed in an evening problem session on Thursday 30 September from 5--7 PM in vV 901. The problems to be discussed will be
The second homework, consisting of the problems
The third homework, consisting of the problems
