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arXiv · 0909.5548

Extending hyperelliptic K3 surfaces, and Godeaux surfaces with torsion Z/2

Stephen Coughlan
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Abstract

We study the extension of a hyperelliptic K3 surface to a Fano 6-fold. This determines a family of surfaces of general type with p_g=1, K^2=2 and hyperelliptic canonical curve, where each surface is a weighted complete intersection inside a Fano 6-fold. Finally, we use these hyperelliptic surfaces to determine an 8-parameter family of Godeaux surfaces with torsion Z/2.

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Stephen Coughlan. 2009-09-30. Extending hyperelliptic K3 surfaces, and Godeaux surfaces with torsion Z/2. https://arxiv.org/abs/0909.5548

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