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Remarks on BCOV invariants and degenerations of Calabi-Yau manifolds

Kefeng Liu Wei Xia

Differential Geometry mathscidoc:1912.43123

Science China Mathematics, 62, (1), 171-184, 2019.1
For a one parameter family of Calabi-Yau threefolds, Green et al. (2009) expressed the total singularities in terms of the degrees of Hodge bundles and Euler number of the general fiber. In this paper, we show that the total singularities can be expressed by the sum of asymptotic values of BCOV (Bershadsky-Cecotti-Ooguri-Vafa) invariants, studied by Fang et al. (2008). On the other hand, by using Yau's Schwarz lemma, we prove Arakelov type inequalities and Euler number bound for Calabi-Yau family over a compact Riemann surface.
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@inproceedings{kefeng2019remarks,
  title={Remarks on BCOV invariants and degenerations of Calabi-Yau manifolds},
  author={Kefeng Liu, and Wei Xia},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111657820641683},
  booktitle={Science China Mathematics},
  volume={62},
  number={1},
  pages={171-184},
  year={2019},
}
Kefeng Liu, and Wei Xia. Remarks on BCOV invariants and degenerations of Calabi-Yau manifolds. 2019. Vol. 62. In Science China Mathematics. pp.171-184. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111657820641683.
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