The Rank of Syzygies

I will explain a notion of rank for the relations amongst the equations of a projective variety, generalizing the classical notion of rank of a quadric. I will then explain a result telling us that, for a general canonical curve, all syzygies are linear combinations of syzygies of minimal rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank four. As a special case, this perspective gives us a new, and simpler, proof of Green’s conjecture for general curves.

https://harvard.zoom.us/j/91082896381?pwd=TmJCanRPVlM4VGR2L1RzZGVGbHRVQT09