Elliptic genera of toric varieties and applications to mirror symmetry

@article{Borisov2000EllipticGO,
  title={Elliptic genera of toric varieties and applications to mirror symmetry},
  author={Lev Borisov and Anatoly S. Libgober},
  journal={Inventiones mathematicae},
  year={2000},
  volume={140},
  pages={453-485}
}
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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