Non-Collapsible Dual Complexes and Fake del Pezzo Surfaces
Abstract
We propose the new construction of complex surfaces with h1,0 = h2,0 = 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 h1,1 = 9 (presumably Barlow surface).
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