New construction of a complex surface with h^{1,1}=9 via smoothing of a normal crossing surface with non-collapsible duncehat dual complex, claimed to be the Barlow surface.
Smoothings of Fano varieties with normal crossing singularities
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abstract
This paper obtains criteria for a Fano variety X with normal crossing singularities defined over an algebraically closed field of characteristic zero, to be smoothable. The difference with the original version is that the theory of logarithmic structures and deformations is used in order to prove that X is smoothable by a smooth variety, if and only if T^1(X)=O_D, where D is the singular locus of X.
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Non-Collapsible Dual Complexes and Fake del Pezzo Surfaces
New construction of a complex surface with h^{1,1}=9 via smoothing of a normal crossing surface with non-collapsible duncehat dual complex, claimed to be the Barlow surface.