Remarks on degenerations of hyperkähler manifolds and OG10 -- Giulia Saccà, December 8, 2017

I will present some applications of joint work with J. Kollár, R. Laza, and C. Voisin which studies degenerations of hyperkähler (HK) manifolds. I will show how these results give a new proof that the HK compactification of the Intermediate Jacobian fibration associated to a cubic fourfold is deformation equivalent to O'Grady's 10--dimensional exceptional example (OG10). Finally, I will show how these results, together with Beauville's method for counting curves on K3 surfaces can be used to obtain a very quick calculation of the Euler number of OG10 (part of joint work in progress with K. Hulek and R. Laza).