Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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EXTENDING HYPERELLIPTIC K3 SURFACES, AND GODEAUX SURFACES WITH π1 = ℤ/2

  • Coughlan, Stephen (Institut fur Algebraische Geometrie Leibniz Universitat Hannover)
  • Received : 2015.05.19
  • Published : 2016.07.01
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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 ${\pi}_1={\mathbb{Z}}/2$.

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Acknowledgement

Supported by : National Research Foundation of Korea

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