Degenerations of exotic Calabi-Yau metrics through Atiyah's flop

Abstract: The goal of this talk is to present the construction of new families of complete Calabi-Yau metrics with maximal volume growth on the small resolutions of the ordinary double point singularity in dimension 3. These metrics have tangent cone $\mathbb{C} ×(\mathbb{C}^2/\mathbb{Z}_2)$ at infinity and are parametrised by their Kähler class. As the Kähler class degenerates, the metrics converge in the pointed Gromov-Hausdorff sense to a singular Calabi-Yau metric with an isolated conical singularity modelled on the Stenzel metric at the ordinary double point, thereby providing a new metric realisation of the Atiyah flop. As we will explain, this construction is meant to provide a local adiabatic model for certain degenerations of compact Calabi-Yau manifolds.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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