A Surface Degeneration With Non-Collapsible Contractible Dual Complex

Abstract

We construct a smoothing of a particular normal crossing surface, which dual complex is a duncehat, thus obtaining an example of a surface degeneration with non-collapsible, contractible dual complex. The general fiber of this family has h 1,0 = h 2,0 = 0 and h 1,1 = 9, we conjecture that it is in the deformation class of the Barlow surface. This text is a complete rewrite of author's previous work [14].