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arXiv · 1506.03529

The Craighero-Gattazzo surface is simply-connected

Julie Rana·Jenia Tevelev·Giancarlo Urzúa
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Abstract

We show that the Craighero-Gattazzo surface, the minimal resolution of an explicit complex quintic surface with four elliptic singularities, is simply-connected. This was conjectured by Dolgachev and Werner, who proved that its fundamental group has a trivial profinite completion. The Craighero-Gattazzo surface is the only explicit example of a smooth simply-connected complex surface of geometric genus zero with ample canonical class. We hope that our method will find other applications: to prove a topological fact about a complex surface we use an algebraic reduction mod p technique and deformation theory.

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Julie Rana, Jenia Tevelev, Giancarlo Urzúa. 2015-06-11. The Craighero-Gattazzo surface is simply-connected. https://doi.org/10.1112/s0010437x16008125

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