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.
Categories: math.AG