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arXiv · 1408.6562

The moduli space of asymptotically cylindrical Calabi-Yau manifolds

Ronan J. Conlon·Rafe Mazzeo·Frédéric Rochon
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Abstract

We prove that the deformation theory of compactifiable asymptotically cylindrical Calabi-Yau manifolds is unobstructed. This relies on a detailed study of the Dolbeault-Hodge theory and its description in terms of the cohomology of the compactification. We also show that these Calabi-Yau metrics admit a polyhomogeneous expansion at infinity, a result that we extend to asymptotically conical Calabi-Yau metrics as well. We then study the moduli space of Calabi-Yau deformations that fix the complex structure at infinity. There is a Weil-Petersson metric on this space which we show is K\"ahler. By proving a local families L^2 index theorem, we exhibit its K\"ahler form as a multiple of the curvature of a certain determinant line bundle.

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Ronan J. Conlon, Rafe Mazzeo, Frédéric Rochon. 2014-08-27. The moduli space of asymptotically cylindrical Calabi-Yau manifolds. https://arxiv.org/abs/1408.6562

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