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Fundamental groups of open \(K3\) surfaces, Enriques surfaces and Fano 3-folds. (English) Zbl 1060.14057

From the text: We investigate when the fundamental group of the smooth part of a \(K3\) surface or Enriques surface with Du Val singularities is finite. As a corollary we give an effective upper bound for the order of the fundamental group of the smooth part of a certain Fano 3-fold. This result supports the following conjecture:
Let \(V\) be a \(\mathbb{Q}\)-Fano \(n\)-fold. Then the topological fundamental group \(\pi_1 (V^0)\) of the smooth part \(V^0\) of \(V\) is finite.
This conjecture is still open when the dimension is at least 4, but it would imply that every log terminal Fano variety has a finite fundamental group.

MSC:

14J28 \(K3\) surfaces and Enriques surfaces
14F35 Homotopy theory and fundamental groups in algebraic geometry
14J45 Fano varieties
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References:

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