Projective models for Hilbert squares of $K3$ surfaces

Ángel David Ríos Ortiz, Andrés Rojas, Jieao Song

For a very general polarized $K3$ surface $S\subset {\mathbb{P}}^g$ of genus $g\ge 5$, we study the linear system on the Hilbert square $S^{[2]}$ parametrizing quadrics in $\mathbb{P…