Math 581HA-582HA-583HA
Advanced Algebraic Geometry
Sándor Kovács
Autumn 2003, Winter 2004, Spring 2004 Monday-Thursday 3:30-4:45
This is intended as a ``hands-on'' course, with a lot of
interaction between the students and the instructor. A central element of the
course is solving problems and discussing their solutions. It is suggested
that a student interested in specializing in algebraic geometry should take
all three quarters in the sequence. However, according to plans, the quarters
will cover different topics, so someone interested only in certain parts
should be able to join the course at a later time.
581A: Cohomology (Aut): Cech cohomology, Serre duality, flat and
smooth morphisms, comparison theorems for cohomology.
582A: Curves (Win): Riemann-Roch Theorem, elliptic curves,
embeddings of curves, basic classification.
583A: Surfaces (Spr): Riemann-Roch Theorem,
intersection theory, ruled surfaces, birational transformations, and basic
birational classification.
Prerequisites: Basic knowledge of
algebraic geometry on the level of 507/8, or instructor's permission.
Text: Algebraic Geometry by Robin Hartshorne, GTM 52,
Springer-Verlag.