WHAT: The time has finally come when
I have to teach my own subject! Yikes!

Togliatti Surface

(quintic with 31 ordinary
double points)

Algebraic geometry: the study
of the geometry of solution sets of systems of polynomial equations. Sounds
simple enough doesn’t it? It turns out that while the first steps and
ideas in algebraic geometry are indeed simple and clear, in order to make further
progress the theory took a turn in the direction of high abstraction. On the
one hand, this expanded the reach of algebraic geometry to a much broader scope
interacting withmany more areas of
mathematics (there is hardly any area of mathematics that has been left
untouched by algebraic geometers, or that has not been affected by the
developments of algebraic geometry); on the other hand, it made algebraic
geometry a difficult to approach subject. The goal of this first semester is to
go back to the origins of the subject in order to capture the initial geometric
ideas and motivations – but keeping an eye to how these ideas give birth
to the modern formulations and technological traits of the theory. The
following book provides a nice skeleton for achieving this goal, and you are
all encouraged to grab a copy of it!

HOMEWORK (really? Really!)

There are several good
exercises in the book and we will be mostly drawing from that pool!