Remarks on BCOV invariants and degenerations of Calabi-Yau manifolds
arXiv:1801.06281
Abstract
For a one parameter family of Calabi-Yau threefolds, Green, Griffiths and Kerr have 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 invariants, studied by Fang, Lu and Yoshikawa. 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.
arXiv comment17 pages; accepted for publication in SCIENCE CHINA Mathematics; all comments welcome