2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166364A Danilov-Gizatullin surface is a normal affine surface V, which is a complement to an ample section S in a Hirzebruch surface of index d. By a surprising result due to Danilov and Gizatullin, V depends only on the self-intersection number of S and neither on d nor on S. In this note we provide a new and simple proof of this Isomorphism Theorem.6 pagesAlgebraic Geometry14R05, 14R20text