Non-Collapsible Dual Complexes and Fake del Pezzo Surfaces

Abstract

We propose the new construction of complex surfaces with $h^{1,0}=h^{2,0}=0$ from smoothings of normal crossing surfaces with non-collapsible dual complexes and carry it out for the simplest case of the duncehat complex, obtaining the surface with $h^{1,1}=9$ (presumably Barlow surface).

20 pages, 10 figures, third version. Completely changed the arguments relevant to d-semistability and the obstruction mapping from the incorrect ones

Cited by in corpus (1)

• A Surface Degeneration With Non-Collapsible Contractible Dual Complex