Asymptotic curvature of moduli spaces for Calabi-Yau threefolds

Details Asymptotic curvature of moduli spaces for Calabi-Yau threefolds Asymptotic curvature of moduli spaces for Calabi-Yau threefolds

2009-02-26

arxiv.org/abs/0902.4611v4

Mathematics

Algebraic Geometry

18 pages, minor further changes in v3 and v4

Scientific paper

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.

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