A type of the Lefschetz hyperplane section theorem on -Fano 3-folds with Picard number one and 1/2(1,1,1)-singularities

Abstract

We prove a type of the Lefschetz hyperplane section theorem on -Fano 3-folds with Picard number one and -singularities by using some degeneration method. As a byproduct, we obtain a new example of a Calabi-Yau 3-fold X with Picard number one whose invariants are (H-X(3), c(2)(X) . H-X, e(X)) = (8, 44, -88), where H-X , e(X) and c(2)(X) are an ample generator of Pic(X), the topological Euler characteristic number and the second Chern class of X respectively.