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The classification of hyperelliptic threefolds. (English) Zbl 1473.14074

Summary: We complete the classification of hyperelliptic threefolds, describing in an elementary way the hyperelliptic threefolds with group \(D_4\). These are algebraic and form an irreducible 2-dimensional family.

MSC:

14J30 \(3\)-folds
14J50 Automorphisms of surfaces and higher-dimensional varieties
32Q15 Kähler manifolds
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References:

[1] F. Catanese and P. Corvaja, Teichmüller spaces of generalized hyperelliptic manifolds. In D. Angella, C. Medori, and A. Tomassini (eds.),Complex and symplectic geometry.(Cortona, 2016.) Springer INdAM Series, 21. Springer, Cham, 2017, 39-49. Zbl 1391.32022 MR 3645304 · Zbl 1391.32022
[2] F. Catanese and A. Demleitner, Hyperelliptic threefolds with groupD4, the dihedral group of order8. Preprint, 2018.arXiv:1805.01835[math.AG]
[3] K. Dekimpe, M. Hałenda, and A. Szczepański, Kähler flat manifolds.J. Math. Soc. Japan61(2009), no. 2, 363-377.Zbl 1187.53051 MR 2532893 · Zbl 1187.53051
[4] A. Fujiki, Finite automorphism groups of complex tori of dimension two.Publ. Res. Inst. Math. Sci.24(1988), no. 1, 1-97.Zbl 0654.32015 MR 0944867 · Zbl 0654.32015
[5] H. Lange, Hyperelliptic varieties.Tohoku Math. J.(2)53(2001), no. 4, 491-510. Zbl 1072.14526 MR 1862215 · Zbl 1072.14526
[6] K. Uchida and H. Yoshihara, Discontinuous groups of affine transformations ofC3. Tohoku Math. J.(2)28(1976), no. 1, 89-94.Zbl 0352 · Zbl 0352.20032
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