Geodesic
Fermat's Cubic, Klein's Quartic and Rigid Complex Manifolds of Kodaira Dimension One
Documenta mathematica, Tome 25 (2020), pp. 1241-1262
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For each n≥3 we provide an n-dimensional rigid compact complex manifold of Kodaira dimension 1. First we constructed a series of singular quotients of products of (n−1) Fermat curves with the Klein quartic, which are rigid. Then using toric geometry a suitable resolution of singularities is constructed and the deformation theories of the singular model and of the resolutions are compared, showing the rigidity of the resolutions.
DOI : 10.4171/dm/775
Classification : 14B05, 14B12, 14J10, 14J40, 14L30, 14M25, 32G07, 32J15
Mots-clés : deformation theory, toric geometry, rigid complex manifolds, quotient singularities 
@article{10_4171_dm_775,
     author = {Christian Gleissner and Ingrid Bauer},
     title = {Fermat's {Cubic,} {Klein's} {Quartic} and {Rigid} {Complex} {Manifolds} of {Kodaira} {Dimension} {One}},
     journal = {Documenta mathematica},
     pages = {1241--1262},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/775},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/775/}
}
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Christian Gleissner; Ingrid Bauer. Fermat's Cubic, Klein's Quartic and Rigid Complex Manifolds of Kodaira Dimension One. Documenta mathematica, Tome 25 (2020), pp. 1241-1262. doi: 10.4171/dm/775

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