##### Department of Mathematics,

University of California San Diego

****************************

### Math 208 - Algebraic Geometry

## Gavril Farkas

#### Humbolt Universit"at, Berlin

## Green's Conjecture via Koszul modules.

##### 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.

Host: Prof. Elham Izadi

### April 24, 2020

### 2:00 PM

### Contact Prof J. McKernan for the Zoom URL

****************************