J FUNCTIONS, NON-NEF TORIC VARIETIES AND EQUIVARIANT LOCAL MIRROR SYMMETRY OF CURVES

2006/03/31 by Brian Forbes, Masao Jinzenji · 14 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algorithm #Equivariant map #Factorization #Geometry #Mathematical analysis #Mathematics #Mirror symmetry #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Scheme (mathematics) #Symmetry (geometry) #Theoretical physics #hep-th #math.AG #msc:14N35 #msc:32G20

paper · pdf · doi:10.1142/s0217751x0703649x

published in International Journal of Modern Physics A 22(13), 2327-2360 (World Scientific) · 31 pages, no figures, minor errors in Section 2 and Section 3 are corrected

arxiv created 2006/04/11 · openalex publication_date 2007/05/20 · arxiv updated 2010/10/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We provide a straightforward computational scheme for the equivariant local mirror symmetry of curves, i.e. mirror symmetry for [Formula: see text] for k ≥ 1, and detail related methods for dealing with mirror symmetry of non-nef toric varieties, based on the theorems of Refs. 2 and 13. The basic tools are equivariant I functions and their Birkhoff factorization.

Citations

• Mirror Symmetry and Algebraic Geometry
• Central charges, symplectic forms, and hypergeometric series in local mirror symmetry
• Black hole attractors and the topological string
• Elliptic Gromov - Witten invariants and the generalized mirror conjecture
• Mirror principle I