On Equivariant Elliptic Genera of Toric Calabi-Yau 3-folds

2015/10/29 by Jian Zhou, Zhou, Jian
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.AG

paper · pdf · doi:10.48550/arxiv.1510.08528

arxiv created 2015/10/29 · openalex publication_date 2015/10/29 · arxiv updated 2015/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that equivariant elliptic genera of toric Calabi-Yau 3-folds are generalized weak Jacobi forms. We also introduce a notion of averaged equivariant elliptic genera of toric Calabi-Yau 3-folds, and show that they are ordinary weak Jacobi forms given by an explicit formula predicted by Eguchi and Sugawara.

Citations

• A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications

Related

• Curve counting on elliptic Calabi-Yau threefolds via derived categories
• Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms
• Equivariant Elliptic Genera
• Elliptic genera, real algebraic varieties and quasi-Jacobi forms
• Topological String on elliptic CY 3-folds and the ring of Jacobi forms