Algebraic Geometry Notes
This is a course in algebraic geometry. Actually, it is two courses,
consisting of notes from a yearlong course that didn't get
far enough (2002-03), and a brisk treatment from a course
(in progress, Spring 2010)
in which I am *determined* to get to the cohomology of coherent sheaves,
as well as some interesting properties of curves,
surfaces and toric varieties. Of course, this means risking the wrath
of the Bourbaki police.
It is pre-Hartshorne, a cross between Mumford's Red Book (minus schemes) and
Shafarevich's Basic Algebraic Geometry.
My feeling is that by focusing on complex varieties,
I am able to more clearly point out the relationship between
commutative algebra and the geometry of varieties, and to get to properties
of curves and surfaces without drowning the students in abstraction.
Obviously, it would make better "Bourbaki" sense to start with
Grothendieck's theory of schemes from the beginning, but
it has been my experience that this approach
(even in Mumford's Red Book) overwhelms all but the
very best graduate students and results in an unsatisfying
first-year course. It remains to be seen, of course, whether this approach
fares any better. But hope springs eternal.