Abstract.
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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Oblatum 12-V-1999 & 4-XI-1999¶Published online: 21 February 2000
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Borisov, L., Libgober, A. Elliptic genera of toric varieties and applications to mirror symmetry. Invent. math. 140, 453–485 (2000). https://doi.org/10.1007/s002220000058
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DOI: https://doi.org/10.1007/s002220000058