Intermediate Jacobian of Gushel–Mukai threefolds

Gushel–Mukai threefolds are prime Fano threefolds of genus 6. In the talk I will discuss their geometry and show that their intermediate Jacobian of such $X$ is isomorphic to the Albanese variety of the Hilbert scheme of conics on $X$. This is a joint work in progress with Olivier Debarre.