3 dec 2015 -- 11:00
Aula F, Dip.Matematica, Università "Roma Tre", Roma
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.