Resumen de An intrinsic construction of the principal component of the Hilbert scheme

David Rydh, Roy Mikael Skjelnes

• The principal component of the Hilbert scheme of n points on a scheme X is the closure of the open subset parameterizing n distinct points. In this article we construct the principal component as a certain blow-up of the symmetric product of X. Our construction is based on a local explicit analysis of ´etale families, from which the appropriate universal property, needed to identify the principal component with the blow-up, is derived.