2009/02/26 by Thomas Trenner, Trenner, Thomas, P. M. H. Wilson +2 · 3 citations
Mathematics · #14J32 (Primary) 32Q25 #53A15 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Calabi–Yau manifold #Conjecture #Curvature #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Limit (mathematics) #Mathematical analysis #Mathematics #Metric (unit) #Mirror symmetry #Moduli space #Pure mathematics #Scalar curvature #math.AG #math.DG #msc:14J32 #msc:32Q25 #msc:53A15
paper · pdf · doi:10.48550/arxiv.0902.4611
published in arXiv (Cornell University) (Cornell University) · 18 pages, minor further changes in v3 and v4
openalex publication_date 2009/02/26 · arxiv created 2010/07/19 · arxiv updated 2010/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
Motivated by the classical statements of Mirror Symmetry, we study certain Kahler metrics on the complexified Kahler cone of a Calabi-Yau threefold, conjecturally corresponding to approximations to the Weil-Petersson metric near large complex structure limit for the mirror. In particular, the naturally defined Riemannian metric (defined via cup-product) on a level set of the Kahler cone is seen to be analogous to a slice of the Weil-Petersson metric near large complex limit. This enables us to give counterexamples to a conjecture of Ooguri and Vafa that the Weil-Petersson metric has non-positive scalar curvature in some neighbourhood of the large complex structure limit point.