2005/05/20 by Victor V. Batyrev, Victor Batyrev, Maximilian Kreuzer +2 · 2 citations
Mathematics · Physics and Astronomy · #14J32 #14M25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.AG #math.AT #msc:14J32 #msc:14M25
paper · pdf · doi:10.48550/arxiv.math/0505432
18 pages, AMS-LaTeX
arxiv created 2005/05/20 · openalex publication_date 2005/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 H2 and H3 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^*