|
The main theme of these lectures is to present recent progress
on syzygies of curves using geometric methods. The first lectures will
deal with the basics of Koszul cohomology and the statements of the Green
respectively Green-Lazarsfeld secant conjectures. Voisin's solution to the
generic Green Conjecture will be sketched. Then, I will describe
the implications of Green's Conjecture to the moduli space of curves, and
how using the moduli space, one can prove Green's Conjecture for curves on
arbitary K3 surfaces. Finally I will present a generalization to Green's
Conjecture to paracanonical curves and sketch a solution using special K3
surfaces.
Lecture 1: Thursday 3 December, 11-13, Room F. Lecture 2: Thursday 17 December, 11-13, Room F. |