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Elliptic genera of toric varieties and applications to mirror symmetry

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Inventiones mathematicae Aims and scope

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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Authors and Affiliations

  1. Department of Mathematics, Columbia University, New York, NY 10027, USA¶(e-mail: lborisov@math.columbia.edu), , , , , , US

    Lev A. Borisov

  2. Department of Mathematics, University of Illinois, Chicago, IL 60607, USA¶(e-mail: libgober@math.uic.edu), , , , , , US

    Anatoly Libgober

Authors
  1. Lev A. Borisov
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  2. Anatoly Libgober
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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

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