Green’s conjecture via Koszul modules
Gavril Farkas (Humboldt University of Berlin)
Abstract: Using ideas from geometric group theory we provide a novel approach to Green’s Conjecture on syzygies of canonical curves. Via a strong vanishing result for Koszul modules we deduce that a general canonical curve of genus g satisfies Green’s Conjecture when the characteristic is zero or at least $(g+2)/2$. Our results are new in positive characteristic (and answer positively a conjecture of Eisenbud and Schreyer), whereas in characteristic zero they provide a different proof for theorems first obtained in two landmark papers by Voisin. Joint work with Aprodu, Papadima, Raicu and Weyman.
Audience: researchers in the topic
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