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arXiv · 2012.10995

A Surface Degeneration With Non-Collapsible Contractible Dual Complex

Lev Soukhanov
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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].

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Lev Soukhanov. 2020-12-20. A Surface Degeneration With Non-Collapsible Contractible Dual Complex. https://arxiv.org/abs/2012.10995

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