Asymptotic curvature of moduli spaces for Calabi-Yau threefolds

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• P.M.H. Wilson (Cambridge)
• Wednesday 28 April 2010, 14:15-15:15
• MR13, CMS.

If you have a question about this talk, please contact Burt Totaro.

This talk will describe recent work by the speaker and his research student Thomas Trenner, which in turn follows on from previous work by the speaker on the geometry of Kahler moduli for Calabi-Yau threefolds.

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 structure limit. This enables us to give counterexamples to a conjecture of Ooguri and Vafa that the Weil-Petersson metric has non-positive curvature in some neighbourhood of the large complex structure limit point.

This talk is part of the Algebraic Geometry Seminar series.

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