2009/02/26 by Trenner, Thomas, Wilson, P. M. H.
#14J32 (Primary) 32Q25 #53A15 (Secondary) #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.0902.4611
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.