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

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

2009-09-30

arxiv.org/abs/0909.5548v1

Mathematics

Algebraic Geometry

27 pages

Scientific paper

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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