From koc@ECE.ORST.EDU Sun Mar  4 11:14:02 2001
Date: Sun, 04 Mar 2001 11:13:30 -0800
From: Cetin Kaya Koc <koc@ECE.ORST.EDU>
To: ISLMAIL <islmail@security.ece.orst.edu>
Subject: Mathematics 649: Introduction to Algebraic Geometry (Spring 2001)


Spring 2001.
Mathematics 649. Introduction to Algebraic Geometry, MW 1-2:20.

Textbook: I. R. Shafarevich, Basic Algebraic Geometry, vol. 1,
Springer-Verlag, 1994.

Prerequisites: A course in abstract algebra or instructor's permission.

Analytic geometry studies solution sets of polynomial equations
f(x, y) = 0 or g(x, y, z) = 0, where f and g are polynomials of
degree 1 or 2.  Algebraic geometry begins where analytic geometry
leaves off: it studies solution sets to polynomial equations
of degree d in n variables, where d and n are arbitrary positive
integers (and more generally, to systems of such polynomial
equations).  The subject originated in the mid-19th century
with the study of higher-degree curves in the plane and has
witness an explosion of creative activity in the second half
of the 20th century, including such high points
of 20th-century mathematics as the proofs of the resolution
of singularities theorem by Hironaka, Mordell's conjecture
by Faltings, and Fermat's last theorem by Wiles and Taylor.
In the past thirty years algebraic geometry has also been
extensively used in applications, ranging from computer
graphycs and cryptography to theoretical physics.

A negative side effect of this recent wave of creative activity
in algebraic geometry is that the subject has become more
technical and consequently, more difficult to enter.
The goal of this class is to give an accessible introduction.
to algebraic geometry. We shall concentrate on classical material
from the 19th and early 20th century. Topics will be chosen
from the following list:

Plane curves (including rational and elliptic curves);

affine, projective and quasi-projective varieties;

Krull dimension and the fiber dimension theorem;

local geometry (including smoothness and normality);

intersection of algebraic varieties and Bezout's theorem.

If you have questions about this class, please contact
the instructor at zinovy@math.orst.edu