Quadrics on Gushel-Mukai varieties

Abstract: We study Hilbert schemes of quadrics of dimension $k \in {0,1,2,3}$ on smooth Gushel-Mukai varieties $X$ of dimension $n \in {2,3,4,5,6}$ by relating them to the relative Hilbert schemes of linear subspaces of dimension $k + 1$ of a certain family, naturally associated with $X$, of quadrics of dimension $n - 1$ over the blowup of $\mathbf{P}^5$ at a point.