Some Calabi-Yau coverings over singular varieties and new Calabi-Yau threefolds with Picard rank one

Abstract. This paper is a report on the observation that some singular varieties admit Calabi-Yau coverings. We derive a formula for calculating the invariants of the coverings with degeneration methods. By applying these to Takagi’s Q-Fano examples([Ta1], [Ta2]), we construct several Calabi-Yau threefolds with Picard number one. It turns out that at least 22 of them are new. A Calabi-Yau manifold is a compact Kähler manifold with trivial canonical class such that the intermediate cohomologies of its structure sheaf are all trivial (h i (X, OX) = 0 for 0 < i < dim(X)). One handy way of construction of Calabi-Yau manifolds is by taking coverings of some smooth varieties