Elliptic genera of toric varieties and applications to mirror symmetry

Lev A. Borisov, Anatoly Libgober

Research output: Contribution to journalArticlepeer-review

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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.

Original languageEnglish (US)
Pages (from-to)453-485
Number of pages33
JournalInventiones Mathematicae
Issue number2
StatePublished - 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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