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http://dx.doi.org/10.4134/JKMS.j150307

EXTENDING HYPERELLIPTIC K3 SURFACES, AND GODEAUX SURFACES WITH π1 = ℤ/2  

Coughlan, Stephen (Institut fur Algebraische Geometrie Leibniz Universitat Hannover)
Publication Information
Journal of the Korean Mathematical Society / v.53, no.4, 2016 , pp. 869-893 More about this Journal
Abstract
We construct the extension of a hyperelliptic K3 surface to a Fano 6-fold with extraordinary properties in moduli. This leads us to a family of surfaces of general type with $p_g=1$, q = 0, $K^2=2$ and hyperelliptic canonical curve, each of which is a weighted complete inter-section inside a Fano 6-fold. Finally, we use these hyperelliptic surfaces to determine an 8-parameter family of Godeaux surfaces with ${\pi}_1={\mathbb{Z}}/2$.
Keywords
surfaces of general type; Godeaux surfaces; Fano 6-folds;
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