2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213622We prove that the Dolgachev surface E(1)_{2,3} admits a handlebody decomposition without 1- and 3- handles, and we draw the explicit picture of this handlebody. We also locate a "cork" inside of E(1)_{2,3}, so that E(1)_{2,3} is obtained from E(1) by twisting along this cork.52 pages 46 figures. A new theorem about the cork structure of the Dolgachev surface is addedGeometric TopologyAlgebraic Geometry58D27, 58A05, 57R65text