Green’s conjecture via Koszul modules

Gavril Farkas (Humboldt University of Berlin)

Fri Apr 17, 18:00-19:30 (6 weeks ago)

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.

algebraic geometry

Audience: researchers in the topic

Stanford algebraic geometry seminar

Series comments: Seminar meets 11-12:30 pm pacific time when there is just one talk, and 10:45-11:45 and 12-1 pm pacific time when there is a double header.

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Organizers: Isabel Vogt*, Ravi Vakil*
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