Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds

Details Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds

2005-05-20

arxiv.org/abs/math/0505432v1

Mathematics

Algebraic Geometry

18 pages, AMS-LaTeX

Scientific paper

In this paper, we compute the integral cohomology groups for all examples of Calabi-Yau 3-folds obtained from hypersurfaces in 4-dimensional Gorenstein toric Fano varieties. Among 473 800 776 families of Calabi-Yau 3-folds $X$ corresponding to 4-dimensional reflexive polytopes there exist exactly 32 families having non-trivial torsion in $H^*(X, \Z)$. We came to an interesting observation that the torsion subgroups in $H^2$ and $H^3$ are exchanged by the mirror symmetry involution, i.e. the torsion subgroup in the Picard group of $X$ is isomorphic to the Brauer group of the mirror $X^*$

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