Geodesic
Fermat's Cubic, Klein's Quartic and Rigid Complex Manifolds of Kodaira Dimension One
Documenta mathematica, Tome 25 (2020), pp. 1241-1262.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

For each $n \geq 3$ 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.
Classification : 14J10, 14B12, 14L30, 14M25, 32J15, 32G07, 14J40, 14B05
Keywords: rigid complex manifolds, deformation theory, quotient singularities, toric geometry 
@article{DOCMA_2020__25__a32,
     author = {Bauer, Ingrid and Gleissner, Christian},
     title = {Fermat's {Cubic,} {Klein's} {Quartic} and {Rigid} {Complex} {Manifolds} of {Kodaira} {Dimension} {One}},
     journal = {Documenta mathematica},
     pages = {1241--1262},
     publisher = {mathdoc},
     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a32/}
}
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Bauer, Ingrid; Gleissner, Christian. Fermat's Cubic, Klein's Quartic and Rigid Complex Manifolds of Kodaira Dimension One. Documenta mathematica, Tome 25 (2020), pp. 1241-1262. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a32/