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arXiv · 1906.10610

Non-Collapsible Dual Complexes and Fake del Pezzo Surfaces

Lev Soukhanov
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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).

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Lev Soukhanov. 2019-06-25. Non-Collapsible Dual Complexes and Fake del Pezzo Surfaces. https://arxiv.org/abs/1906.10610

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