Geometry and Arithmetic of Certain Double Octic Calabi–Yau Manifolds
Canadian mathematical bulletin, Tome 48 (2005) no. 2, pp. 180-194
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We study Calabi–Yau manifolds constructed as double coverings of ${{\mathbb{P}}^{3}}$ branched along an octic surface. We give a list of 87 examples corresponding to arrangements of eight planes defined over $\mathbb{Q}$ . The Hodge numbers are computed for all examples. There are 10 rigid Calabi–Yau manifolds and 14 families with ${{h}^{1,2}}\,=\,1.$ The modularity conjecture is verified for all the rigid examples.
Cynk, Sławomir; Meyer, Christian. Geometry and Arithmetic of Certain Double Octic Calabi–Yau Manifolds. Canadian mathematical bulletin, Tome 48 (2005) no. 2, pp. 180-194. doi: 10.4153/CMB-2005-016-7
@article{10_4153_CMB_2005_016_7,
author = {Cynk, S{\l}awomir and Meyer, Christian},
title = {Geometry and {Arithmetic} of {Certain} {Double} {Octic} {Calabi{\textendash}Yau} {Manifolds}},
journal = {Canadian mathematical bulletin},
pages = {180--194},
year = {2005},
volume = {48},
number = {2},
doi = {10.4153/CMB-2005-016-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-016-7/}
}
TY - JOUR AU - Cynk, Sławomir AU - Meyer, Christian TI - Geometry and Arithmetic of Certain Double Octic Calabi–Yau Manifolds JO - Canadian mathematical bulletin PY - 2005 SP - 180 EP - 194 VL - 48 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-016-7/ DO - 10.4153/CMB-2005-016-7 ID - 10_4153_CMB_2005_016_7 ER -
%0 Journal Article %A Cynk, Sławomir %A Meyer, Christian %T Geometry and Arithmetic of Certain Double Octic Calabi–Yau Manifolds %J Canadian mathematical bulletin %D 2005 %P 180-194 %V 48 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-016-7/ %R 10.4153/CMB-2005-016-7 %F 10_4153_CMB_2005_016_7
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