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

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dc.creatorBatyrev, Victor
dc.creatorKreuzer, Maximilian
dc.date2005-05-20
dc.date.accessioned2026-07-07T05:20:05Z
dc.date.available2026-07-07T05:20:05Z
dc.descriptionIn 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 $X^*$
dc.description18 pages, AMS-LaTeX
dc.identifierhttps://arxiv.org/abs/math/0505432
dc.identifierhttp://arxiv.org/abs/math/0505432
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75254
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Topology
dc.subject14J32; 14M25
dc.titleIntegral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
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