Elliptic genera of toric varieties and applications to mirror symmetry
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.
- Publication:
-
Inventiones Mathematicae
- Pub Date:
- May 2000
- DOI:
- 10.1007/s002220000058
- arXiv:
- arXiv:math/9904126
- Bibcode:
- 2000InMat.140..453B
- Keywords:
-
- Mathematics - Algebraic Geometry;
- High Energy Physics - Theory;
- 14J32;
- 14M25;
- 81T40
- E-Print:
- 32 pages, LaTeX