Abstract:
The study of free plane algebraic curves has a long history in algebraic
geometry and commutative algebra, going back to the work of Saito in the
1980s. After briefly revising this theory, I will introduce the Bourbaki
number of a plane curve, and invariant that measures how far from being free a
given curve is. I will also discuss three 0-dimensional schemes naturally
associated with a curve and a syzygy for its jacobian, explaining their
geometry and how they are related.
