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Elliptic Genera and Applications to Mirror Symmetry

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arxiv math/9904126 v1 pith:KENIKZF2 submitted 1999-04-22 math.AG hep-th

Lev A. Borisov , Anatoly Libgober This is my paper · ORCID
classification math.AGhep-th
keywords ellipticcalabi-yaugenusmirrorgeneraprooftoricapplications
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The paper contains a proof that elliptic genus of a Calabi-Yau manifold is a Jacobi form, finds in which dimensions the elliptic genus is determined by the Hodge numbers and shows that elliptic genera of a Calabi-Yau hypersurface in a toric variety and its mirror coincide up to sign. The proof of the mirror property is based on the extension of elliptic genus to Calabi-Yau hypersurfaces in toric varieties with Gorenstein singularities.

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  1. Tracking the symmetries of $\mathbb Z_3$-orbifold K3s within the Mathieu groups

    math.AG 2025-04 conditional novelty 7.0 of 10

    The holomorphic symplectic automorphism group of a Z3-orbifold K3 is (Z3)^2 ⋊ Z4, realized inside M12 and M24, and it combines with Kummer symmetries to generate M24.

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