Abstract: I will show how to use K3 surfaces with special geometry
to construct non-symplectic involutions on the Hilbert
scheme of two points on a K3 surface. More precisely
I will consider K3 surfaces with Picard number two that
admits several embeddings as smooth quartics in the 3-dimensional
complex projective space and K3 surfaces with several nodes.
I will then show that the induced involutions on the Hilbert
scheme have strong connections to the famous Beauville involution.
This is a joint work with S. Boissière and A. Cattaneo.