Asymptotic Curvature of Moduli Spaces for Calabi–yau Threefolds
نویسنده
چکیده
Motivated by the classical statements of Mirror Symmetry, we study certain Kähler metrics on the complexified Kähler 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 Kähler cone is seen to be analogous to a slice of the Weil– Petersson metric near large complex structure 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. 2000 AMS Subject Classification: Primary 14J32, Secondary 32Q25, 53A15
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