Quantum correction and the moduli spaces of Calabi-Yau manifolds

Kefeng Liu Changyong Yin

Differential Geometry mathscidoc:1912.43119

arXiv preprint arXiv:1411.0069, 2014.11
We define the quantum correction of the Teichmller space \mathcal {T} of Calabi-Yau manifolds. Under the assumption of no weak quantum correction, we prove that the Teichmller space \mathcal {T} is a locally symmetric space with the Weil-Petersson metric. For Calabi-Yau threefolds, we show that no strong quantum correction is equivalent to that, with the Hodge metric, the image \mathcal {T} of the Teichmller space \mathcal {T} under the period map \mathcal {T} is an open submanifold of a globally Hermitian symmetric space \mathcal {T} of the same dimension as \mathcal {T} . Finally, for Hyperkhler manifold of dimension \mathcal {T} , we find both locally and globally defined families of \mathcal {T} and \mathcal {T} -classes over the Teichmller space of polarized Hyperkhler manifolds.
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  title={Quantum correction and the moduli spaces of Calabi-Yau manifolds},
  author={Kefeng Liu, and Changyong Yin},
  booktitle={arXiv preprint arXiv:1411.0069},
Kefeng Liu, and Changyong Yin. Quantum correction and the moduli spaces of Calabi-Yau manifolds. 2014. In arXiv preprint arXiv:1411.0069. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111643250493679.
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